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Geometry is the branch of mathematics that deals with points, lines, curves, surfaces and shapes. This document provides instructions on how to divide a line segment into equal parts using a ruler, pencil, protector and compass. The example shown divides an 8cm line segment AB into 5 equal parts by first drawing 30 degree angles at A and B, then using a compass to mark 5 arcs from A and B with the same radius, and finally joining the points.

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Math 1260 bisect a line

1) The document provides instructions for bisecting a line in geometry. It describes drawing a straight line AB and using a compass to draw arcs above and below points A and B with the same length.
2) The intersections of the arcs, labeled C and D, are then connected with a straight line.
3) When completed correctly, line CD will meet and bisect line AB perpendicularly into two equal lengths, successfully bisecting the original line.

Practical geometry for class 8th

This document discusses how to construct quadrilaterals given certain measurements. It provides examples of constructing quadrilaterals when given: 1) four sides and one diagonal, 2) two diagonals and three sides, 3) two adjacent sides and three angles, 4) three sides and two included angles, and 5) other special properties. Step-by-step instructions and diagrams are used to demonstrate constructing specific quadrilaterals based on given measurements.

Geometry working with line segments

This document discusses various operations that can be performed on line segments in geometry, including:
1) Drawing a line segment equal to a given segment
2) Adding and subtracting line segments
3) Multiplying a line segment by a scalar value
4) Dividing a line segment into two equal parts using a perpendicular bisector
5) Dividing a line segment into multiple equal parts using Thales' theorem, which involves drawing an auxiliary line and measuring equal distances along it.

Geometrical Area

An isoceles triangle of the same area as triangle ABC was constructed, where AB = 4 cm, angle B = 60 degrees, and AC = 6 cm. The steps were to draw triangle ABC, construct a parallel line EF through C using a set square and scale, draw perpendiculars from A and B to EF to form a rectangle ABHG, note that GH = 4 cm, take the midpoint I of GH, and join AI and BI to form the required isoceles triangle ABI.

Dividing a segment into several equal parts

The document provides instructions to divide a line segment into 5 equal parts. It involves drawing a line from point A at an angle, then using a compass to mark off 5 equal arcs along the line from A to a point C. Arcs are then drawn from A and B using the lengths AC and CB to find their intersection point D. A line from D to B completes the division of the original line segment AB into 5 congruent parts.

Hexagon to triangle

This document is a certificate from Iqbal Training College certifying that Divya Vijayan.V completed a course on transforming a hexagon into an equal area triangle through a series of steps. It describes how the hexagon ABCDEF is first transformed into a pentagon and then a quadrilateral by drawing parallel lines and sliding vertices. Finally, the quadrilateral is transformed into an equal area triangle FGI by the same method. The certificate is signed by the lecturer in mathematics, ASWATHI.R.S, and certifies Divya's participation in the IQBAL TRAINING COLLEGE program.

Parallel Lines & Related Angles(1 Na)

This document summarizes key concepts about angles and parallel lines from Chapter 7 including:
- Identifying different types of angles such as acute, obtuse, right, reflex
- Properties of angles including complementary, supplementary, adjacent, vertical
- Properties of angles formed by parallel lines and transversals including corresponding angles, alternate angles, interior angles
- Examples are provided to illustrate different types of angles and their properties
- Homework assignments are listed asking students to practice finding unknown angles using properties of angles and parallel lines.

Intercept theorem

This document provides instructions for dividing a line segment into an equal number of parts using the intercept theorem. The steps are to: 1) Draw a line from one endpoint of the segment making an acute angle. 2) Take equal measurements along this line using a compass. 3) Join the last measurement point to the other endpoint to create a reference line. 4) Draw lines parallel to the reference line from each measurement point to divide the segment into equal parts. This process works for any number of desired parts.

Math 1260 bisect a line

1) The document provides instructions for bisecting a line in geometry. It describes drawing a straight line AB and using a compass to draw arcs above and below points A and B with the same length.
2) The intersections of the arcs, labeled C and D, are then connected with a straight line.
3) When completed correctly, line CD will meet and bisect line AB perpendicularly into two equal lengths, successfully bisecting the original line.

Practical geometry for class 8th

This document discusses how to construct quadrilaterals given certain measurements. It provides examples of constructing quadrilaterals when given: 1) four sides and one diagonal, 2) two diagonals and three sides, 3) two adjacent sides and three angles, 4) three sides and two included angles, and 5) other special properties. Step-by-step instructions and diagrams are used to demonstrate constructing specific quadrilaterals based on given measurements.

Geometry working with line segments

This document discusses various operations that can be performed on line segments in geometry, including:
1) Drawing a line segment equal to a given segment
2) Adding and subtracting line segments
3) Multiplying a line segment by a scalar value
4) Dividing a line segment into two equal parts using a perpendicular bisector
5) Dividing a line segment into multiple equal parts using Thales' theorem, which involves drawing an auxiliary line and measuring equal distances along it.

Geometrical Area

An isoceles triangle of the same area as triangle ABC was constructed, where AB = 4 cm, angle B = 60 degrees, and AC = 6 cm. The steps were to draw triangle ABC, construct a parallel line EF through C using a set square and scale, draw perpendiculars from A and B to EF to form a rectangle ABHG, note that GH = 4 cm, take the midpoint I of GH, and join AI and BI to form the required isoceles triangle ABI.

Dividing a segment into several equal parts

The document provides instructions to divide a line segment into 5 equal parts. It involves drawing a line from point A at an angle, then using a compass to mark off 5 equal arcs along the line from A to a point C. Arcs are then drawn from A and B using the lengths AC and CB to find their intersection point D. A line from D to B completes the division of the original line segment AB into 5 congruent parts.

Hexagon to triangle

This document is a certificate from Iqbal Training College certifying that Divya Vijayan.V completed a course on transforming a hexagon into an equal area triangle through a series of steps. It describes how the hexagon ABCDEF is first transformed into a pentagon and then a quadrilateral by drawing parallel lines and sliding vertices. Finally, the quadrilateral is transformed into an equal area triangle FGI by the same method. The certificate is signed by the lecturer in mathematics, ASWATHI.R.S, and certifies Divya's participation in the IQBAL TRAINING COLLEGE program.

Parallel Lines & Related Angles(1 Na)

This document summarizes key concepts about angles and parallel lines from Chapter 7 including:
- Identifying different types of angles such as acute, obtuse, right, reflex
- Properties of angles including complementary, supplementary, adjacent, vertical
- Properties of angles formed by parallel lines and transversals including corresponding angles, alternate angles, interior angles
- Examples are provided to illustrate different types of angles and their properties
- Homework assignments are listed asking students to practice finding unknown angles using properties of angles and parallel lines.

Intercept theorem

This document provides instructions for dividing a line segment into an equal number of parts using the intercept theorem. The steps are to: 1) Draw a line from one endpoint of the segment making an acute angle. 2) Take equal measurements along this line using a compass. 3) Join the last measurement point to the other endpoint to create a reference line. 4) Draw lines parallel to the reference line from each measurement point to divide the segment into equal parts. This process works for any number of desired parts.

Geometric construction

This document discusses several geometric constructions including: defining a line segment as part of a line bounded by two endpoints; a circle's circumference; perpendicular lines meeting at a right angle; the perpendicular bisector dividing a line segment into two equal parts with each point being the same distance from the endpoints; drawing a perpendicular line from a point on a line; and bisecting a line segment perpendicularly by drawing arcs. It concludes with an activity to draw a line segment and bisect it perpendicularly using arcs.

10.4 notes

A quadrilateral is a closed shape with four line segments that intersect only at their endpoints. The sum of the interior angles of any quadrilateral is always 360 degrees. This document provides information about different types of quadrilaterals based on their properties, including whether they have parallel sides and equal angles or sides. It also includes formulas for finding the area and perimeter of rectangles.

Golden section of a segment

This presentation describes how to draw the golden section of a line segment using a compass. It involves drawing a perpendicular line at one end of the segment, transferring the length of the segment to mark a point, drawing a perpendicular bisector to find the midpoint, drawing a circle using the midpoint and one point, and where that circle intersects the original segment to mark the golden section. It further explains that the golden section allows for organic growth, with segments able to take on new golden sections as they are further divided.

Presentation Consruction for class 10th

Hii, in this ppt you will find about construction. it is for class 10th. This ppt is based on 10th MATHEMATICS NCERT.

Quadrilateral

The document defines and describes different types of quadrilaterals. It states that a quadrilateral is a closed figure bounded by four line segments. The sum of the interior angles of any quadrilateral is always 360 degrees. The main types of quadrilaterals discussed are trapezium, parallelogram, rectangle, rhombus, square, and kite. Each shape is defined by the properties of the lengths and orientations of its sides.

Ppt 1

This document discusses two methods for finding the area of a quadrilateral. The first method is to divide the quadrilateral into two triangles and find the sum of their areas. The second method involves drawing a diagonal and a parallel line to form a triangle with the same area as the original quadrilateral, so only the area of the triangle needs to be calculated. In conclusion, drawing a triangle of equal area inside a quadrilateral allows the area to be found by calculating just the triangle's area.

Geometric construction

This document provides an overview of geometric constructions. It defines basic geometric elements like points, lines, planes, angles and their properties. It then describes how to construct common geometric shapes like triangles, quadrilaterals, polygons, circles and arcs using compass and straightedge. Specific techniques are presented for drawing shapes given certain parameters, finding bisecting lines and angles, transferring angles, constructing tangents and tangent arcs.

Constructing triangles

1. The document provides instructions for constructing different types of triangles given specific properties: equilateral triangles given one side, isosceles triangles given two sides, scalene triangles given three sides, and right triangles given the hypotenuse and one leg.
2. The steps involve using a compass to draw arcs with the given side lengths and finding the point of intersection to determine the third vertex.
3. Lines are then drawn between the vertices to complete the triangle.

construction (maths)

The document describes several methods for constructing angles and triangles using only a compass and straightedge. It provides step-by-step instructions on how to construct: an angle bisector; common angles like 60 and 90 degrees; equilateral and isosceles triangles given various parameters; and a triangle given its perimeter and two base angles. Justifications are given explaining how each construction method divides angles or lengths as needed to satisfy the required properties.

Roslina

This document provides instructions for students to practice geometric constructions using a straightedge and compass. It includes how to construct angles of 60, 120 degrees and bisectors of angles. Students will learn to construct angles with specific measurements and draw angle bisectors. The lesson explains the steps and includes examples of constructing different angles and their bisectors on example line segments.

Angles and properties for class VII by G R Ahmed

The document defines different types of angles and their properties. It explains what an angle is, how angles are named and measured. It discusses right angles, straight angles, acute angles, obtuse angles and reflex angles. It describes angles on a straight line, angles at a point, intersecting lines, parallel lines, perpendicular lines, vertically opposite angles, corresponding angles and alternate angles. It presents proofs of several theorems regarding the sum of interior and exterior angles of triangles.

Angles

An angle is formed by two rays with a common endpoint called the vertex. Angles are measured in degrees and can be acute, right, obtuse, straight, or reflex depending on their measure. The protractor postulate allows pairing angles with degree measures between 0 and 180 degrees. The angle addition postulate states that if a point is within an angle, the measures of the angles on either side of it will sum to the total angle measure. Adjacent angles share a vertex and side, complementary angles sum to 90 degrees, and vertical angles are opposite angles formed by two lines and are congruent.

Angle for class VI & VII

The document defines different types of angles and their properties. It explains that an angle is formed when two lines meet at a vertex point. Angles can be measured and classified as acute, obtuse, right or reflex depending on their degree measure. The relationships between angles formed by parallel and intersecting lines are also described, including that vertically opposite, corresponding, and alternate angles are equal. Pairs of lines can be intersecting, parallel, or perpendicular.

Quadrilatrals types -sum180

The power point explains the concept of quadrilateral.It also helps us to understand important theorem " the sum of all the angles in a quadrilateral is 180 degrees".

Ovoid from largest axis

This document provides instructions for drawing an ovoid shape upon its largest axis in 7 steps:
1) Divide the given axis AB into six equal parts.
2) Retain points 2 and 5 and discard the others. Draw a perpendicular line from point 2.
3) Draw a green circle from point 2 with radius 2A and a red semicircle from point 2 with radius 2B to find points C,D,E,F.
4) Join points E and F to point 5, extending the lines until the red semicircle.
5) Draw arches from E and F with radii ED and FC until the black lines, finding points P and Q.
6) Draw a circle

Construction class 9

This document discusses various geometric constructions that can be performed using only a compass and straightedge. It explains how to bisect angles and line segments, construct a 60 degree angle, and construct triangles given properties such as the base, a base angle, the sum or difference of the other sides, or the perimeter and two base angles. Constructions are performed through a series of defined steps using arcs drawn with a compass and straight lines drawn with a straightedge, without measuring lengths or angles numerically.

Angles ppt

1) The document defines an angle as being formed by two rays with a common endpoint called the vertex. Angles can have points in their interior, exterior, or on the angle.
2) There are three main ways to name an angle: using three points with the vertex in the middle, using just the vertex point when it is the only angle with that vertex, or using a number within the angle.
3) There are four types of angles: acute, right, obtuse, and straight. Angles are measured in degrees with a full circle being 360 degrees.

My lines

This document defines and provides examples of geometric terms including: lines, line segments, points, parallel lines, complementary angles, supplementary angles, transversal lines, and vertical angles. Complementary angles sum to 90 degrees, while supplementary angles sum to 180 degrees. Vertical angles are opposite and equal.

Maths

1. The document describes several basic geometric constructions including constructing the bisector of an angle, the perpendicular bisector of a line segment, constructing an angle of 60 degrees, and constructing triangles given various parameters.
2. The constructions are explained step-by-step and include diagrams. Justifications for each construction are provided by showing that key angles and lengths are equal based on properties of angles, arcs, radii, and congruent triangles.
3. Six different constructions of triangles are outlined, given combinations of parameters like the base, a base angle, sums or differences of sides, or the perimeter and two base angles.

Engineering graphics 1 Regular

1. The problem provides data about two points A and B of a line AB, including their front and top view angles and the position of B above the horizontal plane.
2. The solution involves drawing the projections of the points A and B, determining the true length (TL) of the line AB, and locating its traces by extending the projections.
3. Key steps include drawing the projections at the given angles, extending lines to find the true length and true inclinations, and drawing the horizontal and vertical traces.

Triangle &types by sides

The power point explains the concept of triangles and its types.It also helps us to understand the types of triangle by its sides.

Classification of triangle

This document provides an overview of triangles, including their basic definition, examples of triangles in everyday objects, different types of angles, and ways to classify triangles based on their angles and side lengths. It defines acute, right, and obtuse angles. It also explains how to determine if line segments are congruent based on their lengths. Finally, it classifies triangles as acute, right, obtuse, scalene, isosceles, or equilateral depending on their angle measures or relationships between side lengths.

Geometric construction

This document discusses several geometric constructions including: defining a line segment as part of a line bounded by two endpoints; a circle's circumference; perpendicular lines meeting at a right angle; the perpendicular bisector dividing a line segment into two equal parts with each point being the same distance from the endpoints; drawing a perpendicular line from a point on a line; and bisecting a line segment perpendicularly by drawing arcs. It concludes with an activity to draw a line segment and bisect it perpendicularly using arcs.

10.4 notes

A quadrilateral is a closed shape with four line segments that intersect only at their endpoints. The sum of the interior angles of any quadrilateral is always 360 degrees. This document provides information about different types of quadrilaterals based on their properties, including whether they have parallel sides and equal angles or sides. It also includes formulas for finding the area and perimeter of rectangles.

Golden section of a segment

This presentation describes how to draw the golden section of a line segment using a compass. It involves drawing a perpendicular line at one end of the segment, transferring the length of the segment to mark a point, drawing a perpendicular bisector to find the midpoint, drawing a circle using the midpoint and one point, and where that circle intersects the original segment to mark the golden section. It further explains that the golden section allows for organic growth, with segments able to take on new golden sections as they are further divided.

Presentation Consruction for class 10th

Hii, in this ppt you will find about construction. it is for class 10th. This ppt is based on 10th MATHEMATICS NCERT.

Quadrilateral

The document defines and describes different types of quadrilaterals. It states that a quadrilateral is a closed figure bounded by four line segments. The sum of the interior angles of any quadrilateral is always 360 degrees. The main types of quadrilaterals discussed are trapezium, parallelogram, rectangle, rhombus, square, and kite. Each shape is defined by the properties of the lengths and orientations of its sides.

Ppt 1

This document discusses two methods for finding the area of a quadrilateral. The first method is to divide the quadrilateral into two triangles and find the sum of their areas. The second method involves drawing a diagonal and a parallel line to form a triangle with the same area as the original quadrilateral, so only the area of the triangle needs to be calculated. In conclusion, drawing a triangle of equal area inside a quadrilateral allows the area to be found by calculating just the triangle's area.

Geometric construction

This document provides an overview of geometric constructions. It defines basic geometric elements like points, lines, planes, angles and their properties. It then describes how to construct common geometric shapes like triangles, quadrilaterals, polygons, circles and arcs using compass and straightedge. Specific techniques are presented for drawing shapes given certain parameters, finding bisecting lines and angles, transferring angles, constructing tangents and tangent arcs.

Constructing triangles

1. The document provides instructions for constructing different types of triangles given specific properties: equilateral triangles given one side, isosceles triangles given two sides, scalene triangles given three sides, and right triangles given the hypotenuse and one leg.
2. The steps involve using a compass to draw arcs with the given side lengths and finding the point of intersection to determine the third vertex.
3. Lines are then drawn between the vertices to complete the triangle.

construction (maths)

The document describes several methods for constructing angles and triangles using only a compass and straightedge. It provides step-by-step instructions on how to construct: an angle bisector; common angles like 60 and 90 degrees; equilateral and isosceles triangles given various parameters; and a triangle given its perimeter and two base angles. Justifications are given explaining how each construction method divides angles or lengths as needed to satisfy the required properties.

Roslina

This document provides instructions for students to practice geometric constructions using a straightedge and compass. It includes how to construct angles of 60, 120 degrees and bisectors of angles. Students will learn to construct angles with specific measurements and draw angle bisectors. The lesson explains the steps and includes examples of constructing different angles and their bisectors on example line segments.

Angles and properties for class VII by G R Ahmed

The document defines different types of angles and their properties. It explains what an angle is, how angles are named and measured. It discusses right angles, straight angles, acute angles, obtuse angles and reflex angles. It describes angles on a straight line, angles at a point, intersecting lines, parallel lines, perpendicular lines, vertically opposite angles, corresponding angles and alternate angles. It presents proofs of several theorems regarding the sum of interior and exterior angles of triangles.

Angles

An angle is formed by two rays with a common endpoint called the vertex. Angles are measured in degrees and can be acute, right, obtuse, straight, or reflex depending on their measure. The protractor postulate allows pairing angles with degree measures between 0 and 180 degrees. The angle addition postulate states that if a point is within an angle, the measures of the angles on either side of it will sum to the total angle measure. Adjacent angles share a vertex and side, complementary angles sum to 90 degrees, and vertical angles are opposite angles formed by two lines and are congruent.

Angle for class VI & VII

The document defines different types of angles and their properties. It explains that an angle is formed when two lines meet at a vertex point. Angles can be measured and classified as acute, obtuse, right or reflex depending on their degree measure. The relationships between angles formed by parallel and intersecting lines are also described, including that vertically opposite, corresponding, and alternate angles are equal. Pairs of lines can be intersecting, parallel, or perpendicular.

Quadrilatrals types -sum180

The power point explains the concept of quadrilateral.It also helps us to understand important theorem " the sum of all the angles in a quadrilateral is 180 degrees".

Ovoid from largest axis

This document provides instructions for drawing an ovoid shape upon its largest axis in 7 steps:
1) Divide the given axis AB into six equal parts.
2) Retain points 2 and 5 and discard the others. Draw a perpendicular line from point 2.
3) Draw a green circle from point 2 with radius 2A and a red semicircle from point 2 with radius 2B to find points C,D,E,F.
4) Join points E and F to point 5, extending the lines until the red semicircle.
5) Draw arches from E and F with radii ED and FC until the black lines, finding points P and Q.
6) Draw a circle

Construction class 9

This document discusses various geometric constructions that can be performed using only a compass and straightedge. It explains how to bisect angles and line segments, construct a 60 degree angle, and construct triangles given properties such as the base, a base angle, the sum or difference of the other sides, or the perimeter and two base angles. Constructions are performed through a series of defined steps using arcs drawn with a compass and straight lines drawn with a straightedge, without measuring lengths or angles numerically.

Angles ppt

1) The document defines an angle as being formed by two rays with a common endpoint called the vertex. Angles can have points in their interior, exterior, or on the angle.
2) There are three main ways to name an angle: using three points with the vertex in the middle, using just the vertex point when it is the only angle with that vertex, or using a number within the angle.
3) There are four types of angles: acute, right, obtuse, and straight. Angles are measured in degrees with a full circle being 360 degrees.

My lines

This document defines and provides examples of geometric terms including: lines, line segments, points, parallel lines, complementary angles, supplementary angles, transversal lines, and vertical angles. Complementary angles sum to 90 degrees, while supplementary angles sum to 180 degrees. Vertical angles are opposite and equal.

Maths

1. The document describes several basic geometric constructions including constructing the bisector of an angle, the perpendicular bisector of a line segment, constructing an angle of 60 degrees, and constructing triangles given various parameters.
2. The constructions are explained step-by-step and include diagrams. Justifications for each construction are provided by showing that key angles and lengths are equal based on properties of angles, arcs, radii, and congruent triangles.
3. Six different constructions of triangles are outlined, given combinations of parameters like the base, a base angle, sums or differences of sides, or the perimeter and two base angles.

Engineering graphics 1 Regular

1. The problem provides data about two points A and B of a line AB, including their front and top view angles and the position of B above the horizontal plane.
2. The solution involves drawing the projections of the points A and B, determining the true length (TL) of the line AB, and locating its traces by extending the projections.
3. Key steps include drawing the projections at the given angles, extending lines to find the true length and true inclinations, and drawing the horizontal and vertical traces.

Geometric construction

Geometric construction

10.4 notes

10.4 notes

Golden section of a segment

Golden section of a segment

Presentation Consruction for class 10th

Presentation Consruction for class 10th

Quadrilateral

Quadrilateral

Ppt 1

Ppt 1

Geometric construction

Geometric construction

Constructing triangles

Constructing triangles

construction (maths)

construction (maths)

Roslina

Roslina

Angles and properties for class VII by G R Ahmed

Angles and properties for class VII by G R Ahmed

Angles

Angles

Angle for class VI & VII

Angle for class VI & VII

Quadrilatrals types -sum180

Quadrilatrals types -sum180

Ovoid from largest axis

Ovoid from largest axis

Construction class 9

Construction class 9

Angles ppt

Angles ppt

My lines

My lines

Maths

Maths

Engineering graphics 1 Regular

Engineering graphics 1 Regular

Triangle &types by sides

The power point explains the concept of triangles and its types.It also helps us to understand the types of triangle by its sides.

Classification of triangle

This document provides an overview of triangles, including their basic definition, examples of triangles in everyday objects, different types of angles, and ways to classify triangles based on their angles and side lengths. It defines acute, right, and obtuse angles. It also explains how to determine if line segments are congruent based on their lengths. Finally, it classifies triangles as acute, right, obtuse, scalene, isosceles, or equilateral depending on their angle measures or relationships between side lengths.

triangle

This document defines and describes different types of triangles. It begins by introducing triangles and their key components: three vertices, three sides, and three angles that sum to 180 degrees. It then defines acute, right, and obtuse triangles based on whether their angles are less than, equal to, or greater than 90 degrees. In closing, it thanks the reader.

Angles (Geometry 3_1)

This document defines and explains key concepts about angles including:
1) Opposite rays form an angle and have only their endpoints in common. The figure formed is also called a straight angle.
2) An angle is formed when two non-collinear rays share a common endpoint, called the vertex. The two rays are the sides of the angle.
3) An angle separates a plane into three parts: the interior, exterior, and the angle itself. Points inside the angle are in the interior, outside are in the exterior, and on the angle are on the angle.

Types Of Triangles

This document discusses different types of triangles based on side lengths. It defines equilateral triangles as having three equal sides, isosceles triangles as having two equal sides, and scalene triangles as having no equal sides. It then provides examples of side lengths that do and do not form valid triangles.

Lines and angles

This document provides an overview of key concepts related to lines, angles, and shapes in geometry:
1. It defines lines, line segments, and angles, and explains how they are labeled.
2. It describes parallel and perpendicular lines, and explores properties like corresponding angles.
3. It covers calculating and classifying angles, such as complementary, supplementary, and vertically opposite angles.
4. It examines angles in triangles and quadrilaterals, noting the sums of interior and exterior angles.

Angle Relationships Power Point

The document discusses various angle relationships including:
- Defining acute, obtuse, right, and straight angles
- Explaining how to name angles based on their vertices
- Classifying pairs of angles as complementary, supplementary, or neither based on their degree measures
- Using properties of complementary and supplementary angles to find the measure of a missing angle

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.

Information processing cycle

The document discusses the information processing cycle which consists of 4 steps: (1) input - entering data into the computer using devices like keyboards, mice, and scanners, (2) processing - performing operations on the data using the central processing unit (CPU) which interprets instructions and processes data, (3) output - displaying or producing the processed data, and (4) storage - saving the processed data in the computer's memory. The CPU, which can be a microprocessor, is the key component that executes programs and provides computers with their programmability.

Classifying Angles

This document discusses different types of angles including acute, obtuse, right, and straight angles. It defines an angle as being formed by two rays sharing an endpoint called the vertex. Angles are measured in degrees, with acute angles between 0-90 degrees, obtuse angles between 90-180 degrees, right angles equal to 90 degrees, and a straight angle equaling 180 degrees. It includes examples of each type of angle and encourages identifying them in a game.

Lines and angles

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Geometry presentation

Geometry is the branch of mathematics concerned with properties of points, lines, angles, curves, surfaces and solids. It involves visualizing shapes, sizes, patterns and positions. The presentation introduced basic concepts like different types of lines, rays and angles. It also discussed plane figures from kindergarten to 8th grade, including classifying shapes by number of sides. Space figures like cubes and pyramids were demonstrated by having students construct 3D models. The concepts of tessellation, symmetry, and line of symmetry were explained.

Bermuda Triangle

The document discusses the mystery of the Bermuda Triangle and various theories about what causes ships and planes to disappear in this area. It notes several notable incidents like Flight 19 when 5 planes disappeared in 1945. It outlines supernatural theories involving the lost city of Atlantis or sea monsters. It also provides scientific explanations like compass variations, Gulf Stream currents, rogue waves, methane hydrates, human error, and hurricanes. While the causes remain mysterious, the document examines both supernatural and scientific perspectives on the phenomena in the Bermuda Triangle.

ppt on Triangles Class 9

1. The document defines triangles and their properties including three sides, three angles, and three vertices.
2. It explains five criteria for determining if two triangles are congruent: side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and right-angle-hypotenuse-side (RHS).
3. Some properties of triangles discussed are: angles opposite equal sides are equal, sides opposite equal angles are equal, and the sum of any two sides is greater than the third side.

Lesson Plan PowerPoint Presentation

This document provides guidance on developing effective lesson plans. It discusses key components to consider, including knowing your students, the content, and available materials and equipment. Lesson plans should have clear objectives, outline the procedure and activities, and include assessments tied to the objectives. The document also presents several common lesson plan models, such as Gagne's nine events of instruction and the 5E model. Readers are encouraged to design lesson plans that incorporate useful instructional strategies and techniques.

Triangle &types by sides

Triangle &types by sides

Classification of triangle

Classification of triangle

triangle

triangle

Angles (Geometry 3_1)

Angles (Geometry 3_1)

Types Of Triangles

Types Of Triangles

Lines and angles

Lines and angles

Angle Relationships Power Point

Angle Relationships Power Point

Plane Geometry

Plane Geometry

Information processing cycle

Information processing cycle

Classifying Angles

Classifying Angles

Lines and angles

Lines and angles

Geometry presentation

Geometry presentation

Bermuda Triangle

Bermuda Triangle

ppt on Triangles Class 9

ppt on Triangles Class 9

Telling the time ppt

Telling the time ppt

Lesson Plan PowerPoint Presentation

Lesson Plan PowerPoint Presentation

Lecture_4-Slides_(Part_1).pptx

This document provides an overview of geometric construction concepts including:
- The principles of geometric construction using only a ruler and compass.
- Key terminology related to points, lines, angles, planes, circles, polygons and other basic geometric entities.
- Procedures for performing common geometric constructions such as bisecting lines, arcs and angles, constructing perpendiculars and parallels, dividing lines into equal parts, and constructing tangencies.

Construction of maths class 9th

This document discusses various geometric constructions that can be performed using only a compass and ruler. It explains how to bisect angles and line segments, construct a 60 degree angle, and construct triangles given different combinations of side lengths or angles. Specifically, it provides step-by-step instructions on how to construct a triangle if given its base, one base angle, and the sum of the other two sides; or given its base, a base angle, and the difference between the other two sides; or given its perimeter and two base angles.

Class 5 presentation

The document provides information for an engineering class including the instructor's name and class details, assignments due dates and details, and content on surveying techniques and geometric constructions. Key points covered include potential errors in surveying, definitions of surveying, examples of historical errors, instructions for groups to practice drawing techniques, and methods for drawing various geometric shapes and their intersections.

Buksis 7.1 new

This document provides information about angles and how to identify, measure, and classify different types of angles. It discusses key angle terms like acute, obtuse, right, and straight angles. It also explains how to use a protractor to measure angles and introduces different angle relationships formed when two lines are intersected by a transversal, such as corresponding angles, alternate interior angles, and vertical angles. Students are provided examples to estimate and measure angles, identify angle components, and investigate angle properties.

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This document provides instructions for performing various geometric constructions. It begins with an introduction on the importance of geometric constructions in engineering drawing. It then covers techniques for constructing lines, angles, triangles, circles, quadrilaterals, regular polygons, tangents to circles, joining circles, ellipses, and involutes. The document provides detailed step-by-step instructions for over 30 different geometric constructions, with diagrams to illustrate each method. Accuracy is emphasized as the main difficulty in geometric constructions.

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This document defines a locus as a set of points that satisfy certain geometric conditions. It provides examples of loci that are: a given distance from a point or line, equidistant from two points or lines, perpendicular or parallel to a given line, or satisfy other angle or distance criteria. The objectives are to identify loci using a compass, ruler, and protractor. Several examples are worked out step-by-step to illustrate how to construct loci for points satisfying different conditions. Independent practice problems are provided for students to construct their own loci diagrams.

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Engg engg academia_commonsubjects_drawingunit-i

1. The document discusses scales used in engineering drawings. It defines representative fraction and describes different types of scales including plane, diagonal, and triangular scales.
2. Construction techniques for various scales are provided, along with examples of how to construct a 1:4 scale and a diagonal scale of 3:200.
3. Common geometric constructions used in engineering drawings are also outlined, such as bisecting lines and angles, drawing perpendicular and parallel lines, and constructing regular polygons.

geometry m1

This document covers different topics in geometry including points, lines, line segments, rays, angles, and measuring angles. It defines each term and provides examples. Points have position but no size, a line extends indefinitely, a line segment connects two points, a ray has an endpoint and extends in one direction, and an angle is formed by two rays with a common endpoint. The document explains how to measure angles using a protractor and the degree unit, and provides practice examples of finding the measure of different angles.

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The document provides instructions for geometric constructions of various shapes and figures in engineering drawing, including:
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- Methods for constructing parallel lines, perpendicular lines, dividing a line into equal parts, bisecting angles, drawing arcs and circles through three points.
- Specific steps are outlined for constructing regular polygons like triangles, squares, pentagons, and hexagons given the length of their sides or the diameter of a circumscribing circle. The document also provides a method for constructing a regular polygon with any number of sides.

ADG (Geometrical Constructions).pptx

The document provides instructions for performing various geometric constructions using drawing instruments. It covers constructing lines, angles, triangles, quadrilaterals, circles, ellipses, parabolas, hyperbolas and their tangents. The methods include using a compass, set squares, concentric circles and the distance squared rule. Instructions are given step-by-step with diagrams to divide lines into ratios, bisect angles, construct perpendiculars, inscribe and circumscribe shapes, draw tangents and join two points with a curve. The document also introduces graphic language components, drawing instruments and their use in technical drawing and sketching.

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The document discusses parallel, intersecting, and perpendicular lines. It defines each type of line and provides examples. Parallel lines never cross. Intersecting lines meet at a common point. Perpendicular lines intersect each other at right angles. The document describes three methods for drawing perpendicular lines using a set square, protractor, or compass. It includes examples of applying each method.

STRAND 3.0 GEOMETRY.pptx cbc grade 6 for leaners

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geometricalconstruction-101112193228-phpapp01.pptx

This document provides instructions for performing various geometric constructions. It begins with introductory information on points, lines, and common geometric shapes. It then provides step-by-step instructions for constructing angles, triangles, circles, quadrilaterals, regular polygons, tangents to circles, joining circles, ellipses, involutes, and more. The constructions require only a compass and straightedge. Accuracy is emphasized as the key difficulty.

Engineering Drawing - Chapter 1.pdf

The document provides an overview of Engineering Drawing - MEng 2031. It introduces basic concepts like graphical language, technical drawing, lettering, and line types. It describes standards for drawings and sheet sizes. It explains techniques for geometric constructions like triangles, polygons, circles, tangents, and ellipses. The purpose of engineering drawing is to communicate designs through accurate graphic representations.

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The document provides instructions for drawing an isometric square with each side equal to the diameter of a circle. It explains how to draw the horizontal and vertical center lines of the square and its diagonals. It then gives directions to draw construction lines from two corners to the midpoint of another side, and to use the intersections as centers to draw arcs with a compass to complete the four corners of the isometric square.

EG(sheet 4- Geometric construction).pptx

The document discusses various geometric constructions including:
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2. Bisecting a given angle.
3. Inscribing a square in a given circle.
4. Drawing parabolas, cycloids, epicycloids, and hypocycloids by rolling and tracing circles.
Step-by-step methods are provided for each construction without mathematical proofs.

Engineering Graphics - 1.ppt

This document provides an overview of topics related to engineering drawing and graphics. It covers scales, engineering curves, loci of points, orthographic projections, projections of points/lines/planes/solids, sections and developments, intersections of surfaces, and isometric projections. For each topic, it lists subsections that provide definitions, methods, and example problems. The document appears to be part of an online course or reference material for learning the principles and techniques of engineering drawing.

4f. Pedagogy of Mathematics (Part II) - Geometry(Ex 4.6 & 4.7)

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You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"

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Mule event processing models | MuleSoft Mysore Meetup #47

Mule event processing models | MuleSoft Mysore Meetup #47
Event Link:- https://meetups.mulesoft.com/events/details/mulesoft-mysore-presents-mule-event-processing-models/
Agenda
● What is event processing in MuleSoft?
● Types of event processing models in Mule 4
● Distinction between the reactive, parallel, blocking & non-blocking processing
For Upcoming Meetups Join Mysore Meetup Group - https://meetups.mulesoft.com/mysore/YouTube:- youtube.com/@mulesoftmysore
Mysore WhatsApp group:- https://chat.whatsapp.com/EhqtHtCC75vCAX7gaO842N
Speaker:-
Shivani Yasaswi - https://www.linkedin.com/in/shivaniyasaswi/
Organizers:-
Shubham Chaurasia - https://www.linkedin.com/in/shubhamchaurasia1/
Giridhar Meka - https://www.linkedin.com/in/giridharmeka
Priya Shaw - https://www.linkedin.com/in/priya-shaw

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https://app.box.com/s/y977uz6bpd3af4qsebv7r9b7s21935vdclinical examination of hip joint (1).pdf

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This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.

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Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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clinical examination of hip joint (1).pdf

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LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP

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- 2. Q. What is geometry? Answer: Geometry is the branch of mathematics in which we deals with points, lines, curves, surfaces and shapes.
- 3. Q. How many end points of a line segment? Answer: A line segment has two end points.
- 4. Q. How many end points of a line? Answer: A line has no end point.
- 5. Q. How many end points of a ray? Answer: A ray has only one end point.
- 6. Q. How many end points of a ray? Answer: A ray has only one end point.
- 8. Example # 1: Draw a line segment 8cm in length and divide it into 5 equal parts. STEPS OF CONSTRUCTION: • The line segment AB of length 8 cm is drawn. • At A, AX is drawn making an angle of 30° with protector. • Using compasses from point A, 5 arcs are drawn on AX with suitable radius mark their intersection points as C, D, E, F and G. Such that AC = CD = DE = EF = FG. • At B, BY is drawn making an angle of 30° with protector. • Using compasses from point B, 5 arcs are drawn on BY with same radius and mark their intersection points as H, I, J, K and L . Such that BH = HI = IJ = JK = KL. • Join the points A to L, C to K, D to J, E to I, F to H, and G to B. • Hence, line segment AB is divided into 5 equal parts. 8cmA B 30° X 30° C D E F G H I J K L Y
- 9. Q. What we have discussed today? Answer: Dividing a line segment into equal parts.
- 10. Q. Name the instrument which we use for dividing a line segment into equal parts. Answer: We use Ruler, Pencil, Protector and Compass for dividing a line segment into equal parts.
- 11. Q. What is the first step of construction? Answer: Draw a line segment of given length.
- 12. Q. What is the second step of construction? Answer: At point A, draw an angle of 30° with protector.
- 13. Q. What is the third step of construction? Answer: Using compasses from point A, five arcs are marked with suitable radius on AX.
- 14. Q. What is the forth step of construction? Answer: At point B, draw the same angle of 30° with protector.
- 15. Q. What is the fifth step of construction? Answer: Using compasses from point B five arcs are marked with the same radius on BY.
- 16. Q. Which points will join from the given figure? 8cmA B 30° X 30° C D E F G H I J K L Y Answer: Join the points A to L, C to K, D to J, E to I, F to H and G to B.
- 17. Activity • Draw a line segment 6cm in length and divide it into 4 equal parts.

- Prepare by Zaheer Abbasi 06/03/13 Class VII Fazaia Intermediate College
- Prepare by Zaheer Abbasi 06/03/13 Class VII Fazaia Intermediate College