Isosceles triangles (1)
โขDownload as PPT, PDFโข
1 likeโข466 views
The document provides instructions for making isosceles triangles from a rectangular piece of paper. By folding the paper in half and cutting along a line from the top of the fold to the bottom corner, it creates three triangles, one of which has two equal sides, identifying it as an isosceles triangle. The instructions emphasize proving the two sides are equal using folding and symmetry.
Report
Share
Report
Share
Recommended
Isosceles Triangles
The document provides instructions for creating isosceles triangles from a rectangular piece of paper. It has the following steps:
1. Fold a rectangular piece of paper in half and draw a line from the top of the fold to the bottom right corner, cutting along the line.
2. This creates three triangles, with one line of symmetry.
3. By folding along the line of symmetry, it proves that two of the sides of the triangle are equal, identifying it as an isosceles triangle.
4. The instructions then have the reader create another isosceles triangle from the remaining pieces of the original rectangle.
Mathematics: Regular and Irregular Shapes
Use mathematical language to explain the difference between regular and irregular shapes. Regular shapes have sides and angles that are all equal. Irregular shapes have sides and angles of different measures.
Transversals similar figures edmodo
The document discusses similar and congruent triangles. It provides the definitions that two figures are similar if they have the same shape, and for triangles to be similar their corresponding angles must be congruent and corresponding sides must be proportional. It then gives examples of finding missing side lengths of triangles using the properties of similar triangles.
Tutorials--Triangle Area and Perimeter
This document provides 40 examples of calculating the area and perimeter of different types of triangles, including scalene, acute, obtuse, isosceles, equilateral, right triangles and specific right triangles defined by their angles or side lengths. The examples show calculations with measures expressed as both numbers and variables.
4b area of polygons
This document discusses formulas and strategies for computing the perimeter and area of basic shapes like triangles, parallelograms, trapezoids, and circles. It provides the formulas for finding the perimeter of squares, rectangles, and other polygons by adding the side lengths. Formulas are also given for finding the area of triangles, parallelograms, squares, rectangles, trapezoids, circles, and more complex irregular shapes by decomposing them into basic components. Examples are worked through on various pages and homework is assigned covering the material.
Chapter 10 day 1 s.a. of prisms
1. The document discusses geometric concepts related to polyhedrons including prisms. It defines key terms like polyhedron, lateral area, surface area, altitude, net, prism, right prism, and provides formulas to calculate lateral area and surface area of right prisms.
2. Examples are given to identify 3D shapes from their nets and to draw orthographic views of objects. The document also contains classwork on drawing nets and calculating measurements of prisms.
3. Geometric concepts like polyhedrons, prisms, lateral area, surface area, and orthographic views are defined and formulas/examples are provided for calculating measurements and drawing representations of prisms.
002 s.a. of prisms
This document discusses how to find the lateral area and surface area of a polyhedron called a prism. It defines key terms like polyhedron, altitude, lateral area, and net. It then explains that the lateral area of a right prism can be found using the formula LA = Hp, where H is the height and p is the perimeter of the base. The surface area of a right prism can be found using the formula SA = LA + 2B, where LA is the lateral area and B is the area of one base. Examples are provided to demonstrate calculating the lateral area and surface area of a right prism with a regular hexagonal base.
Similar triangles student_handout
The document provides instructions for an activity where students work in groups to cut out triangles from shapes. They sort and group the triangles based on similar characteristics and compare corresponding angles and sides. Students then measure and record side lengths and angle measurements of triangles within each group. They are tasked with labeling additional similar triangles without tools based on given scale factors between pairs of triangles. The purpose is for students to observe properties of similar figures and learn related vocabulary terms like similar figures, corresponding angles and sides, and scale factor.
Recommended
Isosceles Triangles
The document provides instructions for creating isosceles triangles from a rectangular piece of paper. It has the following steps:
1. Fold a rectangular piece of paper in half and draw a line from the top of the fold to the bottom right corner, cutting along the line.
2. This creates three triangles, with one line of symmetry.
3. By folding along the line of symmetry, it proves that two of the sides of the triangle are equal, identifying it as an isosceles triangle.
4. The instructions then have the reader create another isosceles triangle from the remaining pieces of the original rectangle.
Mathematics: Regular and Irregular Shapes
Use mathematical language to explain the difference between regular and irregular shapes. Regular shapes have sides and angles that are all equal. Irregular shapes have sides and angles of different measures.
Transversals similar figures edmodo
The document discusses similar and congruent triangles. It provides the definitions that two figures are similar if they have the same shape, and for triangles to be similar their corresponding angles must be congruent and corresponding sides must be proportional. It then gives examples of finding missing side lengths of triangles using the properties of similar triangles.
Tutorials--Triangle Area and Perimeter
This document provides 40 examples of calculating the area and perimeter of different types of triangles, including scalene, acute, obtuse, isosceles, equilateral, right triangles and specific right triangles defined by their angles or side lengths. The examples show calculations with measures expressed as both numbers and variables.
4b area of polygons
This document discusses formulas and strategies for computing the perimeter and area of basic shapes like triangles, parallelograms, trapezoids, and circles. It provides the formulas for finding the perimeter of squares, rectangles, and other polygons by adding the side lengths. Formulas are also given for finding the area of triangles, parallelograms, squares, rectangles, trapezoids, circles, and more complex irregular shapes by decomposing them into basic components. Examples are worked through on various pages and homework is assigned covering the material.
Chapter 10 day 1 s.a. of prisms
1. The document discusses geometric concepts related to polyhedrons including prisms. It defines key terms like polyhedron, lateral area, surface area, altitude, net, prism, right prism, and provides formulas to calculate lateral area and surface area of right prisms.
2. Examples are given to identify 3D shapes from their nets and to draw orthographic views of objects. The document also contains classwork on drawing nets and calculating measurements of prisms.
3. Geometric concepts like polyhedrons, prisms, lateral area, surface area, and orthographic views are defined and formulas/examples are provided for calculating measurements and drawing representations of prisms.
002 s.a. of prisms
This document discusses how to find the lateral area and surface area of a polyhedron called a prism. It defines key terms like polyhedron, altitude, lateral area, and net. It then explains that the lateral area of a right prism can be found using the formula LA = Hp, where H is the height and p is the perimeter of the base. The surface area of a right prism can be found using the formula SA = LA + 2B, where LA is the lateral area and B is the area of one base. Examples are provided to demonstrate calculating the lateral area and surface area of a right prism with a regular hexagonal base.
Similar triangles student_handout
The document provides instructions for an activity where students work in groups to cut out triangles from shapes. They sort and group the triangles based on similar characteristics and compare corresponding angles and sides. Students then measure and record side lengths and angle measurements of triangles within each group. They are tasked with labeling additional similar triangles without tools based on given scale factors between pairs of triangles. The purpose is for students to observe properties of similar figures and learn related vocabulary terms like similar figures, corresponding angles and sides, and scale factor.
Geometry Terms - 5th Grade
This document defines and describes basic geometry terms including points, lines, line segments, rays, planes, angles, and the relationships between lines such as intersecting, parallel, and perpendicular lines. Points mark exact locations, lines have no endpoints, line segments connect two endpoints, rays have one endpoint and extend in one direction, planes are flat endless surfaces, and angles are formed by two rays with a shared endpoint which can be acute, obtuse, right, or straight.
Triangle
Triangles have three sides and three interior angles. They can be classified based on side length as equilateral (all sides equal), isosceles (two sides equal), or scalene (all sides unequal). Triangles can also be classified based on angle measures as acute (all angles less than 90 degrees), right (one angle of 90 degrees), or obtuse (one angle greater than 90 degrees). The Pythagorean theorem can be used to calculate the length of the hypotenuse (longest side) of a right triangle given the lengths of the other two sides. The area of any triangle can be calculated by multiplying the base by the height.
Welcome To Geometry
This document introduces key concepts in geometry, including points, lines, planes, angles, polygons, triangles, quadrilaterals, and different types of geometric shapes. It defines important vocabulary like parallel lines, intersecting lines, perpendicular lines, acute angles, right angles, and obtuse angles. It also explains how to classify triangles based on angle types (right, acute, obtuse) and side lengths (scalene, isosceles, equilateral). Similarly, it describes how to classify quadrilaterals such as parallelograms, rectangles, rhombi, squares, and trapezoids based on their properties.
Perimeter and Area of Polygons
A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. Area is the quantity that expresses the extent of a two-dimensional region, shape, or planar lamina, in the plane. Surface area is its analog on the two-dimensional surface of a three-dimensional object
Plane Geometry
This document provides an overview of key concepts in plane geometry covered in Chapter 5, including points, lines, planes, angles, parallel and perpendicular lines, triangles, polygons, coordinate geometry, congruence, transformations, and tessellations. Specific topics discussed include classifying angles, properties of parallel lines cut by a transversal, the triangle sum theorem, types of triangles and polygons, finding total angle measures of polygons, and using coordinate geometry. Homework problems are provided at the end of sections for additional practice.
similar triangles
1) Triangles are three-sided polygons formed by three line segments. The sum of the three interior angles is always 180 degrees.
2) There are certain properties that apply to all triangles, such as being rigid flat shapes that satisfy the Triangle Inequality.
3) Triangles can be categorized based on their sides and angles. Congruent triangles are identical in shape and size, while similar triangles have the same shape but may differ in size. The properties of similar triangles can be used to solve proportional relationships.
Mathematics: Perimeter and Area Lesson
This document provides information about polygons, perimeter, and area. It defines a polygon as a 2D shape with straight sides. There are two types of polygons: regular and irregular. Perimeter is defined as the distance around a 2D shape and is measured by adding up the lengths of all sides. Area is the amount of surface a shape covers and is measured in square units. Formulas are provided to calculate the perimeter and area of common polygons like squares, rectangles, and triangles. Examples are given to demonstrate calculating perimeter and area using the appropriate formulas and units of measurement.
Geometry In The Real World
This power point is a project for Mrs. Sykes, by Canute Jacobsen. The power point itself is about how geometry is involved in the world.
Perimeter
The document defines perimeter and provides formulas for calculating the perimeter of rectangles, squares, and triangles. It explains that perimeter is the distance around a two-dimensional shape. For rectangles, the perimeter formula is P=2(length+breadth). For squares, the formula is P=4xside. For triangles, the formula is P=a+b+c, where a, b, and c are the lengths of the three sides. An example problem calculates the perimeter of a triangular plot of land that is to be fenced with four rounds of wire.
Mathematics: Solids Lesson
This document discusses geometric shapes, specifically comparing and classifying solid shapes according to their dimensions and properties. It explains that solid shapes are three-dimensional objects that can be described by their width, depth, and height. The key properties of solid shapes discussed are their volume, surface area, and the number of vertices, faces, and edges they have. Specific solid shapes are also discussed like cubes, cones, cuboids, spheres, pyramids and prisms along with their nets.
Equal triangles
1) The document discusses different ways to determine if two triangles are equal based on their side lengths and angles.
2) It establishes three general principles: if two triangles have (a) equal sides, (b) two equal sides and the angle between them, or (c) one equal side and equal angles at the ends, then their other properties (sides or angles) are also equal.
3) Examples are given to illustrate each principle and exceptions are noted where equality does not imply full equality.
Triangles
Triangles have three non-collinear points called vertices and three segments connecting them called sides. A triangle is named by listing its three vertices, usually in clockwise order. Triangles are classified based on sides as equilateral, isosceles, or scalene and based on angles as acute, right, obtuse, or equiangular. The sum of the interior angles of any triangle is always 180 degrees. Exterior angles of a triangle are supplementary to their adjacent interior angles.
Geometry Project John Hoang Block 1
This document defines and describes basic geometric shapes and terms including points, lines, planes, angles, triangles, quadrilaterals, circles, cylinders, spheres, and other shapes. It provides the formal definitions for these fundamental concepts in geometry. Key terms are defined such as a point having no size, a line being infinite in length, a plane being a flat surface that extends without thickness, and polygons being shapes with a specific number of sides.
Drawing some kinds of line in triangle
There are four types of lines that can be drawn in a triangle:
1. A perpendicular bisector of a side bisects the side at a 90 degree angle.
2. An angle bisector bisects the interior angle of the triangle into two equal angles.
3. A height or altitude drops perpendicular from a vertex to the opposite side.
4. A median connects a vertex to the midpoint of the opposite side.
Exploring the Pythagorean Relationship
The document explores the Pythagorean relationship through an activity with cut-out squares that form three triangles. Students are asked to measure the sides and angles of the triangles, record the data in a table, and identify which triangles are right triangles based on having a 90 degree angle. For right triangles, students state the relationship between the areas of the squares and describe the relationship between the side lengths as being the Pythagorean relationship, where the area of the hypotenuse square equals the sum of the areas of the other two squares.
Modern Geometry Topics
This powerpoint includes:
Triangles and Quadrangles
Definition, Types, Properties, Secondary part, Congruency and Area
Definitions of Triangles and Quadrangles
Desarguesian Plane
Mathematician Desargues and His Background
Harmonic Sequence of Points/Lines
Illustrations and Animated Lines.
Math
This document provides an overview of elementary shapes in math. It begins by explaining that all shapes are formed using lines and curves and can be organized into categories like lines, angles, and polygons. It then discusses how to measure and compare line segments using observations, tracing, and a ruler. Different types of angles are defined. Two-dimensional shapes like polygons, quadrilaterals, circles and triangles are described. Three-dimensional shapes such as cubes, cuboids, spheres and hemispheres are also defined along with their key features like faces, edges and vertices.
8.6 proportions and similar triangles
This document discusses proportional relationships in triangles and solving proportions. It contains theorems about parallel lines intersecting two sides of a triangle proportionally and a ray bisecting an angle proportioning the sides. It also contains examples of using proportions to solve for variables in triangles and showing lines are parallel. The final sections provide homework problems from specific textbook pages.
MWA 10 6.4 Similar Triangles
- The document discusses similar triangles and provides examples of finding missing side lengths and angles of similar triangles using proportional reasoning.
- Similar triangles are defined as triangles where corresponding angles are congruent or corresponding sides are proportional.
- Examples show setting up proportions between corresponding sides or angles of similar triangles to calculate missing values. One example finds the height of a tree using similar right triangles formed by a person's view in a mirror.
Symmetry
Symmetry is discussed in the document, including line symmetry and mirror reflection. Line symmetry occurs when a figure can be folded along a line so that the two halves are identical mirror images. Mirror reflection produces identical images that are left-right reversals. Figures can have no lines of symmetry, one line, two lines, or multiple lines depending on their shape. Symmetry is important in areas like art, architecture, and design as it produces pleasing proportional balances.
Making Trihexaflexagons
This document provides instructions for creating a trihexaflexagon, a paper model that can be flexed to reveal different faces. It explains how to mark and cut a sheet of paper to form the necessary shapes and labels. Detailed steps are given for folding the paper according to the markings to form a hexagonal shape. Additional instructions describe how to flex the completed model by folding edges together to reveal different triangle combinations on each face.
01 triangle new
1) The document discusses congruent figures and triangles. It defines congruent figures as those with the same shape and size that can be placed directly on top of each other.
2) It explains that triangles are congruent if their three sides or three angles are equal, or if one side and the two angles adjacent to it are equal.
3) It provides examples of congruent and non-congruent triangles based on different combinations of equal sides and angles.
More Related Content
What's hot
Geometry Terms - 5th Grade
This document defines and describes basic geometry terms including points, lines, line segments, rays, planes, angles, and the relationships between lines such as intersecting, parallel, and perpendicular lines. Points mark exact locations, lines have no endpoints, line segments connect two endpoints, rays have one endpoint and extend in one direction, planes are flat endless surfaces, and angles are formed by two rays with a shared endpoint which can be acute, obtuse, right, or straight.
Triangle
Triangles have three sides and three interior angles. They can be classified based on side length as equilateral (all sides equal), isosceles (two sides equal), or scalene (all sides unequal). Triangles can also be classified based on angle measures as acute (all angles less than 90 degrees), right (one angle of 90 degrees), or obtuse (one angle greater than 90 degrees). The Pythagorean theorem can be used to calculate the length of the hypotenuse (longest side) of a right triangle given the lengths of the other two sides. The area of any triangle can be calculated by multiplying the base by the height.
Welcome To Geometry
This document introduces key concepts in geometry, including points, lines, planes, angles, polygons, triangles, quadrilaterals, and different types of geometric shapes. It defines important vocabulary like parallel lines, intersecting lines, perpendicular lines, acute angles, right angles, and obtuse angles. It also explains how to classify triangles based on angle types (right, acute, obtuse) and side lengths (scalene, isosceles, equilateral). Similarly, it describes how to classify quadrilaterals such as parallelograms, rectangles, rhombi, squares, and trapezoids based on their properties.
Perimeter and Area of Polygons
A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. Area is the quantity that expresses the extent of a two-dimensional region, shape, or planar lamina, in the plane. Surface area is its analog on the two-dimensional surface of a three-dimensional object
Plane Geometry
This document provides an overview of key concepts in plane geometry covered in Chapter 5, including points, lines, planes, angles, parallel and perpendicular lines, triangles, polygons, coordinate geometry, congruence, transformations, and tessellations. Specific topics discussed include classifying angles, properties of parallel lines cut by a transversal, the triangle sum theorem, types of triangles and polygons, finding total angle measures of polygons, and using coordinate geometry. Homework problems are provided at the end of sections for additional practice.
similar triangles
1) Triangles are three-sided polygons formed by three line segments. The sum of the three interior angles is always 180 degrees.
2) There are certain properties that apply to all triangles, such as being rigid flat shapes that satisfy the Triangle Inequality.
3) Triangles can be categorized based on their sides and angles. Congruent triangles are identical in shape and size, while similar triangles have the same shape but may differ in size. The properties of similar triangles can be used to solve proportional relationships.
Mathematics: Perimeter and Area Lesson
This document provides information about polygons, perimeter, and area. It defines a polygon as a 2D shape with straight sides. There are two types of polygons: regular and irregular. Perimeter is defined as the distance around a 2D shape and is measured by adding up the lengths of all sides. Area is the amount of surface a shape covers and is measured in square units. Formulas are provided to calculate the perimeter and area of common polygons like squares, rectangles, and triangles. Examples are given to demonstrate calculating perimeter and area using the appropriate formulas and units of measurement.
Geometry In The Real World
This power point is a project for Mrs. Sykes, by Canute Jacobsen. The power point itself is about how geometry is involved in the world.
Perimeter
The document defines perimeter and provides formulas for calculating the perimeter of rectangles, squares, and triangles. It explains that perimeter is the distance around a two-dimensional shape. For rectangles, the perimeter formula is P=2(length+breadth). For squares, the formula is P=4xside. For triangles, the formula is P=a+b+c, where a, b, and c are the lengths of the three sides. An example problem calculates the perimeter of a triangular plot of land that is to be fenced with four rounds of wire.
Mathematics: Solids Lesson
This document discusses geometric shapes, specifically comparing and classifying solid shapes according to their dimensions and properties. It explains that solid shapes are three-dimensional objects that can be described by their width, depth, and height. The key properties of solid shapes discussed are their volume, surface area, and the number of vertices, faces, and edges they have. Specific solid shapes are also discussed like cubes, cones, cuboids, spheres, pyramids and prisms along with their nets.
Equal triangles
1) The document discusses different ways to determine if two triangles are equal based on their side lengths and angles.
2) It establishes three general principles: if two triangles have (a) equal sides, (b) two equal sides and the angle between them, or (c) one equal side and equal angles at the ends, then their other properties (sides or angles) are also equal.
3) Examples are given to illustrate each principle and exceptions are noted where equality does not imply full equality.
Triangles
Triangles have three non-collinear points called vertices and three segments connecting them called sides. A triangle is named by listing its three vertices, usually in clockwise order. Triangles are classified based on sides as equilateral, isosceles, or scalene and based on angles as acute, right, obtuse, or equiangular. The sum of the interior angles of any triangle is always 180 degrees. Exterior angles of a triangle are supplementary to their adjacent interior angles.
Geometry Project John Hoang Block 1
This document defines and describes basic geometric shapes and terms including points, lines, planes, angles, triangles, quadrilaterals, circles, cylinders, spheres, and other shapes. It provides the formal definitions for these fundamental concepts in geometry. Key terms are defined such as a point having no size, a line being infinite in length, a plane being a flat surface that extends without thickness, and polygons being shapes with a specific number of sides.
Drawing some kinds of line in triangle
There are four types of lines that can be drawn in a triangle:
1. A perpendicular bisector of a side bisects the side at a 90 degree angle.
2. An angle bisector bisects the interior angle of the triangle into two equal angles.
3. A height or altitude drops perpendicular from a vertex to the opposite side.
4. A median connects a vertex to the midpoint of the opposite side.
Exploring the Pythagorean Relationship
The document explores the Pythagorean relationship through an activity with cut-out squares that form three triangles. Students are asked to measure the sides and angles of the triangles, record the data in a table, and identify which triangles are right triangles based on having a 90 degree angle. For right triangles, students state the relationship between the areas of the squares and describe the relationship between the side lengths as being the Pythagorean relationship, where the area of the hypotenuse square equals the sum of the areas of the other two squares.
Modern Geometry Topics
This powerpoint includes:
Triangles and Quadrangles
Definition, Types, Properties, Secondary part, Congruency and Area
Definitions of Triangles and Quadrangles
Desarguesian Plane
Mathematician Desargues and His Background
Harmonic Sequence of Points/Lines
Illustrations and Animated Lines.
Math
This document provides an overview of elementary shapes in math. It begins by explaining that all shapes are formed using lines and curves and can be organized into categories like lines, angles, and polygons. It then discusses how to measure and compare line segments using observations, tracing, and a ruler. Different types of angles are defined. Two-dimensional shapes like polygons, quadrilaterals, circles and triangles are described. Three-dimensional shapes such as cubes, cuboids, spheres and hemispheres are also defined along with their key features like faces, edges and vertices.
8.6 proportions and similar triangles
This document discusses proportional relationships in triangles and solving proportions. It contains theorems about parallel lines intersecting two sides of a triangle proportionally and a ray bisecting an angle proportioning the sides. It also contains examples of using proportions to solve for variables in triangles and showing lines are parallel. The final sections provide homework problems from specific textbook pages.
MWA 10 6.4 Similar Triangles
- The document discusses similar triangles and provides examples of finding missing side lengths and angles of similar triangles using proportional reasoning.
- Similar triangles are defined as triangles where corresponding angles are congruent or corresponding sides are proportional.
- Examples show setting up proportions between corresponding sides or angles of similar triangles to calculate missing values. One example finds the height of a tree using similar right triangles formed by a person's view in a mirror.
What's hot (19)
Similar to Isosceles triangles (1)
Symmetry
Symmetry is discussed in the document, including line symmetry and mirror reflection. Line symmetry occurs when a figure can be folded along a line so that the two halves are identical mirror images. Mirror reflection produces identical images that are left-right reversals. Figures can have no lines of symmetry, one line, two lines, or multiple lines depending on their shape. Symmetry is important in areas like art, architecture, and design as it produces pleasing proportional balances.
Making Trihexaflexagons
This document provides instructions for creating a trihexaflexagon, a paper model that can be flexed to reveal different faces. It explains how to mark and cut a sheet of paper to form the necessary shapes and labels. Detailed steps are given for folding the paper according to the markings to form a hexagonal shape. Additional instructions describe how to flex the completed model by folding edges together to reveal different triangle combinations on each face.
01 triangle new
1) The document discusses congruent figures and triangles. It defines congruent figures as those with the same shape and size that can be placed directly on top of each other.
2) It explains that triangles are congruent if their three sides or three angles are equal, or if one side and the two angles adjacent to it are equal.
3) It provides examples of congruent and non-congruent triangles based on different combinations of equal sides and angles.
Modulepolygons
This document provides information about polygons, including defining polygons, recognizing different types of polygons, naming polygons based on the number of sides, and determining key properties such as the number of sides, vertices, and diagonals. It also discusses sketching polygons, identifying lines of symmetry, and the geometric properties of specific polygons like triangles and quadrilaterals. Examples are provided for drawing triangles and quadrilaterals given specific measurements. Key terms are defined in a glossary at the end.
Special quadtilaterals parallelograms
The document summarizes properties of different quadrilaterals and triangles. It defines a parallelogram as a quadrilateral with two sets of opposite parallel sides. Some key properties listed are that opposite angles of a parallelogram are congruent, consecutive angles are supplementary, opposite sides are congruent, and the diagonals bisect each other. A construction method for drawing a parallelogram using parallel lines is also provided.
Special quadtilaterals parallelograms
The document summarizes properties of different shapes including kites, trapezoids, triangles, and parallelograms. It states that the diagonals of a kite are perpendicular and one diagonal bisects the other. It also notes that opposite angles and sides of a parallelogram are congruent, and the diagonals of a parallelogram bisect each other. Finally, it provides classwork and homework assignments related to special quadrilaterals.
COT-1-QUADRILATERALS THAT ARE PARALLELOGRAM.pptx
1) The document describes a 9th grade mathematics classroom observation on geometry and properties of parallelograms. Students were asked to measure sides and angles of a drawn parallelogram and record their findings.
2) Key properties of parallelograms are reviewed, including opposite sides being congruent and parallel, opposite angles being congruent, and diagonals bisecting each other.
3) For a learning task, students are instructed to draw and measure a parallelogram, then make conjectures about measurements and properties.
L4 polygons and_quadrilaterals by unknown
This document provides information about geometry drawing tools and different types of polygons and quadrilaterals. It includes definitions and examples of polygons, types of quadrilaterals, and methods for drawing geometric shapes both freehand and using tools. The document also contains examples of drawing shapes that meet certain criteria and describing shapes based on their properties.
Cross sections of 3 d figures
Cross sections are 2D shapes that result when a 3D figure is cut by a plane. The plane can be parallel or perpendicular to the base of the 3D figure. A horizontal cross section of a cone is a circle, while a vertical cross section is a triangle. Both the horizontal and vertical cross sections of a cylinder are circles and rectangles, respectively.
Geometry unit 1.1.pptx
This document discusses different ways to represent three-dimensional objects using two-dimensional drawings. It introduces nets, which are 2D diagrams that can be folded to form a 3D object. Isometric drawings show a 3D object from a corner view, allowing you to see the top, front and side simultaneously. Orthographic drawings show separate top, front and side views. The document uses examples and problems to illustrate these concepts and techniques for visualizing and analyzing 3D shapes.
Tecnical drawing & polygonal shapes
The document defines and describes various polygons shapes such as triangles, quadrilaterals, trapezoids, and provides examples. It defines triangles as shapes with three straight lines and three vertices whose interior angles sum to 180 degrees. Quadrilaterals are defined as shapes with four straight sides and four angles that sum to 360 degrees. Important lines of triangles like heights, midpoints, and midpoints of segments are defined. Trapezoids are described as quadrilaterals where none of the sides are equal or parallel. Pictures of shapes made of triangles and squares are provided as examples.
Geometry unit 11.1
This document discusses classifying and analyzing three-dimensional geometric shapes. It defines key terms like face, edge, and vertex used to describe three-dimensional shapes. Examples are provided to demonstrate classifying shapes based on these properties, identifying shapes from nets, and describing cross sections. The document also provides examples applying these concepts to cutting cheese into different shapes depending on how it is sliced. Overall, the document covers classifying, analyzing, and describing three-dimensional shapes.
Visualizing solid shapes
It an interesting ppt from with a child can understand the concept of solid shape and different views of a solid shapes from different sides .
thank you
300017-DumalnegNHS-Raval, Cyrah Mae.ppt
This document discusses properties of quadrilaterals including parallelograms, rectangles, rhombuses, and squares. It provides definitions and key properties of each shape. Students are instructed to create a foldable study guide defining and comparing the different quadrilaterals. They will draw examples of each and list their distinguishing properties. The document aims to help students learn the different theorems and identify the characteristics that define special types of parallelograms.
3.8.3 Similar Triangle Properties
The document discusses properties of similar triangles that can be used to find unknown lengths, including:
- The triangle proportionality theorem and its converse, which state that if a line parallel to one side of a triangle intersects the other two sides, it divides them proportionally
- Using ratios to make indirect measurements of objects that can't be directly measured
- Applying the triangle angle bisector theorem to divide opposite sides of a triangle proportionally
- Using scale drawings and similar triangles to solve problems involving proportional relationships between corresponding parts of similar figures
7.4 Similarity in right triangles
This document discusses similar right triangles and the geometric mean. It contains examples and theorems about how cutting an altitude to the hypotenuse of a right triangle divides it into two similar right triangles. The geometric mean of two numbers a and b is the positive number x that satisfies ab=x^2. Using the geometric mean and properties of similar triangles, missing side lengths can be calculated.
COT PPT-ILLUSTRATING TRIANGLE CONGRUENCE.pptx
1. The document discusses the concept of triangle congruence by defining corresponding parts of triangles, illustrating how to determine if two triangles are congruent, and providing examples of congruent triangles in real life such as pyramids and bridges.
2. Students are instructed to complete a tangram puzzle activity by cutting out puzzle pieces and rearranging them to form images, then asked questions about corresponding parts of congruent triangles and given a performance task to create additional tangram puzzles.
3. Triangle congruence is defined as having corresponding sides and angles that are congruent and noted with the symbol โ
, and the key
Circles in Triangles using Geometric Construction
Inscribe circles in triangles using geometric construction, with PC geometry software such as Dr Geo on Linux. This slide show presents some innovative constructions. The slide show and included instructions are public domain. Basic use of compass and straightedge is advised as a prerequisite topic.
Class 4 presentation posted
Here are the steps to draw an equilateral triangle using the diameters method:
1. Draw a circle of any convenient size.
2. Draw two diameters of the circle that intersect at right angles. These will form the bases of the triangle.
3. With the points where the diameters intersect the circle as centers, and using the radius of the circle as the radius, draw arcs above the diameters.
4. The point where the arcs intersect will be the third vertex of the equilateral triangle.
5. Connect this point to the two base points to complete the equilateral triangle.
The key steps are using the diameters of the circle as the bases, and the fact that arcs drawn with the same
Similar to Isosceles triangles (1) (20)
More from Worserbay
Paul klee
Paul Klee was a Swiss artist born in 1879 who worked as an art teacher in Germany. He was known for his abstract paintings that did not always depict recognizable objects and for incorporating children's art into his own work. Klee frequently used warm, cool, and neutral colors in his paintings.
Factorsprimessquare
The document discusses factors and prime numbers. It explains that factors of a number are pairs of numbers that multiply to give that number. It provides examples of finding the factors of numbers like 10, 8, 20, 7, and 36. It notes that a number with only two factors, 1 and itself, is a prime number. It also discusses how square numbers have identical factors and how understanding factors can help with multiplication.
Divisibility rules
This document outlines divisibility rules that can be used to determine if a number is divisible by certain other numbers without performing long division. The rules provided are: a number is divisible by 2 if the last digit is even; divisible by 3 if the sum of the digits is 3, 6, or 9; divisible by 4 if the last two digits are divisible by 4; divisible by 5 if the last digit is 0 or 5; divisible by 6 if it meets the rules for both 2 and 3; divisible by 8 if the last three digits are divisible by 8; divisible by 9 if the sum of the digits is 9; and divisible by 10 if the last digit is 0. There is no simple rule for divisibility by 7
Square roots cube_roots
The document discusses square roots and cube roots. It explains that a square root is a number that when multiplied by itself gives the original number. Similarly, a cube root is a number that when cubed (multiplied by itself three times) gives the original number. Tables of numbers and their squares and cubes are provided as examples. The reader is asked to complete practice problems for square and cube roots.
Mrodd mrseven (1)
This story is about Mr. Odd and Mrs. Even who live in neighboring lands dedicated to odd and even numbers, respectively. When an earthquake hits, it mixes up their lands and possessions. Mr. Odd likes things in odd numbers like 1 dog, 3 turtles, and 5 hammers. Mrs. Even prefers even numbers like 2 rabbits and 4 boys. The story poses math problems about who various groups should live with after their numbers change, like 12 bats or 19 Vikings. In the end, all the characters live happily ever after after sorting out the mixed up lands and items.
Odd and even_numbers
The document provides instructions to write out lists of odd and even numbers within given ranges, continues specified sequences of even numbers, provides odd numbers preceding given even numbers, and asks how many even and odd numbers within ranges end with specific digits.
Greaterthanorlessthan
This document discusses multiples of ten and comparing numbers using greater than and less than symbols. It provides examples of identifying multiples of ten by looking for zeros in the ones place, listing multiples of ten, twenty, and thirty between given numbers, and determining which numbers could be written in covered boxes based on the greater than or less than symbols.
Country temperatures
The document contains 24 lines of numerical data showing country names paired with positive or negative numbers. Some country names are repeated across multiple lines with different paired numbers, suggesting scores or values compared between the listed countries.
Greater less
Charlie the crocodile only eats the largest number he sees. The document asks which number - 5 or 2 - Charlie would try to eat from the set {5, 2}. It then asks how this can be shown mathematically and defines the symbols "greater than" and "less than" which are used to represent whether a number is larger or smaller than another number. It concludes by listing some past meals Charlie has eaten to demonstrate larger and smaller fractions.
Order the numbers
This document contains 4 sections of numbers with checkmarks under each. The first 3 sections have 4 numbers each with checkmarks under the first 3 numbers. The last section has 1 number with checkmarks under the first 3 digits. Instructions below each section direct the reader to either start with the smallest number or start with the largest number.
Fibonacci sequence
This document discusses the Fibonacci sequence, a number pattern discovered over 8000 years ago by Italian mathematician Leonardo Fibonacci. The sequence begins with 0, 1, 1, 2, 3, 5, 8, 13, 21, etc. with each subsequent number calculated by adding the previous two numbers. It explains that this sequence appears throughout nature, such as the spiral patterns of sunflowers and other plants. Activities are provided for students to explore properties of the Fibonacci sequence, like adding numbers above a line in the sequence equalling one less than the number below.
Y5 t2u11 numbersequences
The document discusses recognizing and extending number sequences by identifying rules. It provides examples of ascending and descending number sequences with missing values and asks the reader to determine the missing numbers and rules. It then asks the reader to generate their own sequences with missing values for their partner to solve. The goal is to be able to recognize and extend number sequences as well as explain the rules for sequences both orally and in writing.
Code crackers
This document contains a series of math problems where the student is tasked with identifying the pattern in several number sequences and determining the next number in the sequence. By solving these pattern problems correctly, the student can unlock a prize that is contained in the teacher's safe.
Number sequences
The document discusses different types of number sequences and patterns. It provides examples of sequences where the rule is to add or subtract a constant number, double or halve successive terms, or apply other mathematical functions. Students are asked to identify the rules and extend the sequences by determining missing or subsequent terms. Famous sequences like the Fibonacci sequence are also introduced.
Counting on and_back_y3
The document discusses counting on and back in tens and hundreds. It provides examples of sequences where the numbers increase or decrease by 10 or 100 between each term. Students are asked to identify patterns in sequences and complete number patterns counting on or back by the appropriate amount. They are also prompted to discuss observed patterns with a friend.
Sequences
This document discusses sequences and provides examples of sequences of objects, sounds, letters, and numbers. It explains that a sequence is a pattern and provides tips for identifying the next item in a number sequence, such as looking for the pattern and placing a number in the sequence to check if it looks correct. Several number sequence examples are given, asking the reader to identify the missing numbers.
Understanding negative numbers
The document discusses negative numbers and how they relate to temperature scales. It provides examples of number lines that extend to the left of zero to demonstrate negative numbers. It then shows vertical and horizontal temperature scales and asks questions about finding missing numbers and comparing temperatures on the scales. Finally, it asks the reader to order a set of numbers from coldest to warmest based on their position on the temperature scale.
More from Worserbay (20)
Recently uploaded
Profiles of Iconic Fashion Personalities.pdf
The fashion industry is dynamic and ever-changing, continuously sculpted by trailblazing visionaries who challenge norms and redefine beauty. This document delves into the profiles of some of the most iconic fashion personalities whose impact has left a lasting impression on the industry. From timeless designers to modern-day influencers, each individual has uniquely woven their thread into the rich fabric of fashion history, contributing to its ongoing evolution.
Anny Serafina Love - Letter of Recommendation by Kellen Harkins, MS.
This letter, written by Kellen Harkins, Course Director at Full Sail University, commends Anny Love's exemplary performance in the Video Sharing Platforms class. It highlights her dedication, willingness to challenge herself, and exceptional skills in production, editing, and marketing across various video platforms like YouTube, TikTok, and Instagram.
Business storytelling: key ingredients to a story
Storytelling is an incredibly valuable tool to share data and information. To get the most impact from stories there are a number of key ingredients. These are based on science and human nature. Using these elements in a story you can deliver information impactfully, ensure action and drive change.
The latest Heat Pump Manual from Newentide
๐๐ง๐ฏ๐๐ข๐ฅ ๐ญ๐ก๐ ๐
๐ฎ๐ญ๐ฎ๐ซ๐ ๐จ๐ ๐๐ง๐๐ซ๐ ๐ฒ ๐๐๐๐ข๐๐ข๐๐ง๐๐ฒ ๐ฐ๐ข๐ญ๐ก ๐๐๐๐๐๐๐๐โ๐ฌ ๐๐๐ญ๐๐ฌ๐ญ ๐๐๐๐๐ซ๐ข๐ง๐ ๐ฌ
Explore the details in our newly released product manual, which showcases NEWNTIDE's advanced heat pump technologies. Delve into our energy-efficient and eco-friendly solutions tailored for diverse global markets.
How MJ Global Leads the Packaging Industry.pdf
MJ Global's success in staying ahead of the curve in the packaging industry is a testament to its dedication to innovation, sustainability, and customer-centricity. By embracing technological advancements, leading in eco-friendly solutions, collaborating with industry leaders, and adapting to evolving consumer preferences, MJ Global continues to set new standards in the packaging sector.
Part 2 Deep Dive: Navigating the 2024 Slowdown
Introduction
The global retail industry has weathered numerous storms, with the financial crisis of 2008 serving as a poignant reminder of the sector's resilience and adaptability. However, as we navigate the complex landscape of 2024, retailers face a unique set of challenges that demand innovative strategies and a fundamental shift in mindset. This white paper contrasts the impact of the 2008 recession on the retail sector with the current headwinds retailers are grappling with, while offering a comprehensive roadmap for success in this new paradigm.
Innovation Management Frameworks: Your Guide to Creativity & Innovation
Innovation Management Frameworks: Your Guide to Creativity & InnovationOperational Excellence Consulting
[To download this presentation, visit:
https://www.oeconsulting.com.sg/training-presentations]
This PowerPoint compilation offers a comprehensive overview of 20 leading innovation management frameworks and methodologies, selected for their broad applicability across various industries and organizational contexts. These frameworks are valuable resources for a wide range of users, including business professionals, educators, and consultants.
Each framework is presented with visually engaging diagrams and templates, ensuring the content is both informative and appealing. While this compilation is thorough, please note that the slides are intended as supplementary resources and may not be sufficient for standalone instructional purposes.
This compilation is ideal for anyone looking to enhance their understanding of innovation management and drive meaningful change within their organization. Whether you aim to improve product development processes, enhance customer experiences, or drive digital transformation, these frameworks offer valuable insights and tools to help you achieve your goals.
INCLUDED FRAMEWORKS/MODELS:
1. Stanfordโs Design Thinking
2. IDEOโs Human-Centered Design
3. Strategyzerโs Business Model Innovation
4. Lean Startup Methodology
5. Agile Innovation Framework
6. Doblinโs Ten Types of Innovation
7. McKinseyโs Three Horizons of Growth
8. Customer Journey Map
9. Christensenโs Disruptive Innovation Theory
10. Blue Ocean Strategy
11. Strategynโs Jobs-To-Be-Done (JTBD) Framework with Job Map
12. Design Sprint Framework
13. The Double Diamond
14. Lean Six Sigma DMAIC
15. TRIZ Problem-Solving Framework
16. Edward de Bonoโs Six Thinking Hats
17. Stage-Gate Model
18. Toyotaโs Six Steps of Kaizen
19. Microsoftโs Digital Transformation Framework
20. Design for Six Sigma (DFSS)
To download this presentation, visit:
https://www.oeconsulting.com.sg/training-presentationsย
Unveiling the Dynamic Personalities, Key Dates, and Horoscope Insights: Gemin...
Explore the fascinating world of the Gemini Zodiac Sign. Discover the unique personality traits, key dates, and horoscope insights of Gemini individuals. Learn how their sociable, communicative nature and boundless curiosity make them the dynamic explorers of the zodiac. Dive into the duality of the Gemini sign and understand their intellectual and adventurous spirit.
Satta Matka Dpboss Matka Guessing Kalyan Chart Indian Matka Kalyan panel Chart
Satta Matka Dpboss Matka Guessing Kalyan Chart Indian Matka Kalyan panel ChartโโโโโโโโโโDpboss Matka Guessing Satta Matka Kalyan Chart Indian Matka
SATTA MATKA SATTA FAST RESULT KALYAN TOP MATKA RESULT KALYAN SATTA MATKA FAST RESULT MILAN RATAN RAJDHANI MAIN BAZAR MATKA FAST TIPS RESULT MATKA CHART JODI CHART PANEL CHART FREE FIX GAME SATTAMATKA ! MATKA MOBI SATTA 143 spboss.in TOP NO1 RESULT FULL RATE MATKA ONLINE GAME PLAY BY APP SPBOSSย
The Steadfast and Reliable Bull: Taurus Zodiac Sign
Explore the steadfast and reliable nature of the Taurus Zodiac Sign. Discover the personality traits, key dates, and horoscope insights that define the determined and practical Taurus, and learn how their grounded nature makes them the anchor of the zodiac.
The APCO Geopolitical Radar - Q3 2024 The Global Operating Environment for Bu...
The Radar reflects input from APCOโs teams located around the world. It distils a host of interconnected events and trends into insights to inform operational and strategic decisions. Issues covered in this edition include:
Brian Fitzsimmons on the Business Strategy and Content Flywheel of Barstool S...
On episode 272 of the Digital and Social Media Sports Podcast, Neil chatted with Brian Fitzsimmons, Director of Licensing and Business Development for Barstool Sports.
What follows is a collection of snippets from the podcast. To hear the full interview and more, check out the podcast on all podcast platforms and at www.dsmsports.net
2024-6-01-IMPACTSilver-Corp-Presentation.pdf
IMPACT Silver is a pure silver zinc producer with over $260 million in revenue since 2008 and a large 100% owned 210km Mexico land package - 2024 catalysts includes new 14% grade zinc Plomosas mine and 20,000m of fully funded exploration drilling.
Hamster Kombat' Telegram Game Surpasses 100 Million PlayersโToken Release Sch...
Hamster Kombat' Telegram Game Surpasses 100 Million PlayersโToken Release Schedule Unveiled
NIMA2024 | De toegevoegde waarde van DEI en ESG in campagnes | Nathalie Lam |...
Nathalie zal delen hoe DEI en ESG een fundamentele rol kunnen spelen in je merkstrategie en je de juiste aansluiting kan creรซren met je doelgroep. Door middel van voorbeelden en simpele handvatten toont ze hoe dit in jouw organisatie toegepast kan worden.
Top mailing list providers in the USA.pptx
Discover the top mailing list providers in the USA, offering targeted lists, segmentation, and analytics to optimize your marketing campaigns and drive engagement.
Taurus Zodiac Sign: Unveiling the Traits, Dates, and Horoscope Insights of th...
Dive into the steadfast world of the Taurus Zodiac Sign. Discover the grounded, stable, and logical nature of Taurus individuals, and explore their key personality traits, important dates, and horoscope insights. Learn how the determination and patience of the Taurus sign make them the rock-steady achievers and anchors of the zodiac.
Best Forex Brokers Comparison in INDIA 2024
Navigating the world of forex trading can be challenging, especially for beginners. To help you make an informed decision, we have comprehensively compared the best forex brokers in India for 2024. This article, reviewed by Top Forex Brokers Review, will cover featured award winners, the best forex brokers, featured offers, the best copy trading platforms, the best forex brokers for beginners, the best MetaTrader brokers, and recently updated reviews. We will focus on FP Markets, Black Bull, EightCap, IC Markets, and Octa.
Digital Marketing with a Focus on Sustainability
Digital Marketing best practices including influencer marketing, content creators, and omnichannel marketing for Sustainable Brands at the Sustainable Cosmetics Summit 2024 in New York
Recently uploaded (20)
Anny Serafina Love - Letter of Recommendation by Kellen Harkins, MS.
Anny Serafina Love - Letter of Recommendation by Kellen Harkins, MS.
ย
Innovation Management Frameworks: Your Guide to Creativity & Innovation
Innovation Management Frameworks: Your Guide to Creativity & Innovation
ย
Unveiling the Dynamic Personalities, Key Dates, and Horoscope Insights: Gemin...
Unveiling the Dynamic Personalities, Key Dates, and Horoscope Insights: Gemin...
ย
Satta Matka Dpboss Matka Guessing Kalyan Chart Indian Matka Kalyan panel Chart
Satta Matka Dpboss Matka Guessing Kalyan Chart Indian Matka Kalyan panel Chart
ย
The Steadfast and Reliable Bull: Taurus Zodiac Sign
The Steadfast and Reliable Bull: Taurus Zodiac Sign
ย
The APCO Geopolitical Radar - Q3 2024 The Global Operating Environment for Bu...
The APCO Geopolitical Radar - Q3 2024 The Global Operating Environment for Bu...
ย
Brian Fitzsimmons on the Business Strategy and Content Flywheel of Barstool S...
Brian Fitzsimmons on the Business Strategy and Content Flywheel of Barstool S...
ย
Hamster Kombat' Telegram Game Surpasses 100 Million PlayersโToken Release Sch...
Hamster Kombat' Telegram Game Surpasses 100 Million PlayersโToken Release Sch...
ย
Registered-Establishment-List-in-Uttarakhand-pdf.pdf
Registered-Establishment-List-in-Uttarakhand-pdf.pdf
ย
NIMA2024 | De toegevoegde waarde van DEI en ESG in campagnes | Nathalie Lam |...
NIMA2024 | De toegevoegde waarde van DEI en ESG in campagnes | Nathalie Lam |...
ย
Taurus Zodiac Sign: Unveiling the Traits, Dates, and Horoscope Insights of th...
Taurus Zodiac Sign: Unveiling the Traits, Dates, and Horoscope Insights of th...
ย
Isosceles triangles (1)
- 2. Take a rectangular piece of paper.
- 3. Take a rectangular piece of paper. Fold it in half
- 4. Take a rectangular piece of paper. Fold it in half Use a ruler to draw a line from the top of the fold to the bottom right hand corner.
- 5. Take a rectangular piece of paper. Fold it in half Use a ruler to draw a line from the top of the fold to the bottom right hand corner. Cut along the line.
- 6. You should now have 3 triangles
- 7. Can you prove that this is a line of symmetry?
- 8. Does this triangle have any other line of symmetry?
- 9. No it doesnโt. It only has the one.
- 10. How can we prove that line ac is equal to line bc? a b c d By folding along the line of symmetry. If you havenโt tried it, do it now.
- 11. a b c d b This type of triangle, where two sides are equal, has a special name. It is called an ISOSCELES triangle
- 12. a b c d b Stick this triangle into your jotter and name it ISOSCELES triangle. Now use the other two pieces of the rectangle to make another isosceles triangle.
- 13. Your new triangle should look like this. How do we know it is isoscles?
- 14. Which of these triangles do you think is isosceles?
- 15. These are the isosceles triangles. Write in your jotter how we can describe an isosceles triangle and how we can prove it is isosceles.