8.4 notes
โขDownload as PPT, PDFโข
0 likesโข374 views
1. A quadrilateral is a parallelogram if both pairs of opposite sides are parallel and equal in length. 2. The diagonals of a parallelogram bisect each other. 3. For a quadrilateral to be a parallelogram, the value of x must make both pairs of opposite sides parallel and equal in length.
Report
Share
Report
Share
Recommended
The pythagorean theorem
The document summarizes key information about Pythagoras and the Pythagorean theorem. It explains that Pythagoras lived in 500 BC and is credited with proving the Pythagorean theorem. While the Babylonians understood the relationship between right triangle sides 1000 years prior, Pythagoras is considered the first to provide a formal proof. The theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. Examples are provided to demonstrate how to apply the formula to solve for unknown side lengths of right triangles.
8.4 notes
1) A quadrilateral is a parallelogram if its diagonals bisect each other and both pairs of opposite sides are congruent.
2) For a quadrilateral to be a parallelogram, x must be such that the opposite sides are parallel.
3) Theorems are presented about the properties of rhombuses, rectangles, and squares as special types of parallelograms.
Types of Quadrilateral
A quadrilateral is a polygon with four sides. There are several types of quadrilaterals including trapezoids which have at least one set of parallel opposite sides, parallelograms where both pairs of opposite sides are parallel, rhombuses which have four equal sides, rectangles defined by having four right angles, and squares that are rectangles with four equal sides and angles.
Obj. 27 Special Parallelograms
Prove and apply properties of rectangles, rhombuses, and squares.
Use properties of rectangles, rhombuses, and squares to solve problems.
Prove that a given quadrilateral is a rectangle, rhombus, or square.
Obj. 36 Similar Triangle Properties
Use properties of similar triangles to find segment lengths.
Apply proportionality and triangle angle bisector theorems.
3.9.3 Similar Triangles
This document discusses properties of similar triangles. It defines three ways triangles can be similar: angle-angle similarity (AA~) if two angles of one triangle are congruent to two angles of another; side-side-side similarity (SSS~) if the three sides of one triangle are proportional to the three sides of another; and side-angle-side similarity (SAS~) if two sides of one triangle are proportional to two sides of another and the included angles are congruent. Examples are provided to demonstrate applying these properties to determine if triangles are similar and write similarity statements.
Pythagoreanโs theorem
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs. It can be used to find the missing length of any side of a right triangle when the other two sides are known. For example, if the legs of a right triangle have lengths of 12 and 16, substituting these values into the Pythagorean theorem formula a2 + b2 = c2 allows you to calculate the hypotenuse as 20 by taking the square root of the right side of the equation.
2.7.5 Kites and Trapezoids
This document defines and provides properties of kites and trapezoids. It states that a kite is a quadrilateral with two pairs of congruent consecutive sides, and its diagonals are perpendicular. A trapezoid has one pair of parallel sides called bases, and the nonparallel sides are legs. An isosceles trapezoid has two congruent base angles. The midsegment of a trapezoid is parallel to the bases and is half the sum of the base lengths. Examples are provided to demonstrate solving problems using properties of kites and trapezoids.
Recommended
The pythagorean theorem
The document summarizes key information about Pythagoras and the Pythagorean theorem. It explains that Pythagoras lived in 500 BC and is credited with proving the Pythagorean theorem. While the Babylonians understood the relationship between right triangle sides 1000 years prior, Pythagoras is considered the first to provide a formal proof. The theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. Examples are provided to demonstrate how to apply the formula to solve for unknown side lengths of right triangles.
8.4 notes
1) A quadrilateral is a parallelogram if its diagonals bisect each other and both pairs of opposite sides are congruent.
2) For a quadrilateral to be a parallelogram, x must be such that the opposite sides are parallel.
3) Theorems are presented about the properties of rhombuses, rectangles, and squares as special types of parallelograms.
Types of Quadrilateral
A quadrilateral is a polygon with four sides. There are several types of quadrilaterals including trapezoids which have at least one set of parallel opposite sides, parallelograms where both pairs of opposite sides are parallel, rhombuses which have four equal sides, rectangles defined by having four right angles, and squares that are rectangles with four equal sides and angles.
Obj. 27 Special Parallelograms
Prove and apply properties of rectangles, rhombuses, and squares.
Use properties of rectangles, rhombuses, and squares to solve problems.
Prove that a given quadrilateral is a rectangle, rhombus, or square.
Obj. 36 Similar Triangle Properties
Use properties of similar triangles to find segment lengths.
Apply proportionality and triangle angle bisector theorems.
3.9.3 Similar Triangles
This document discusses properties of similar triangles. It defines three ways triangles can be similar: angle-angle similarity (AA~) if two angles of one triangle are congruent to two angles of another; side-side-side similarity (SSS~) if the three sides of one triangle are proportional to the three sides of another; and side-angle-side similarity (SAS~) if two sides of one triangle are proportional to two sides of another and the included angles are congruent. Examples are provided to demonstrate applying these properties to determine if triangles are similar and write similarity statements.
Pythagoreanโs theorem
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs. It can be used to find the missing length of any side of a right triangle when the other two sides are known. For example, if the legs of a right triangle have lengths of 12 and 16, substituting these values into the Pythagorean theorem formula a2 + b2 = c2 allows you to calculate the hypotenuse as 20 by taking the square root of the right side of the equation.
2.7.5 Kites and Trapezoids
This document defines and provides properties of kites and trapezoids. It states that a kite is a quadrilateral with two pairs of congruent consecutive sides, and its diagonals are perpendicular. A trapezoid has one pair of parallel sides called bases, and the nonparallel sides are legs. An isosceles trapezoid has two congruent base angles. The midsegment of a trapezoid is parallel to the bases and is half the sum of the base lengths. Examples are provided to demonstrate solving problems using properties of kites and trapezoids.
5 lesson 3 rectangles, rhombi, and squares
The document lists the key properties of a parallelogram, rectangle, rhombus, and square. A parallelogram has two pairs of parallel sides, while a rectangle has four right angles and opposite sides that are equal. A rhombus has four equal sides and diagonals that bisect the angles. A square has four equal sides and four equal angles, with diagonals that bisect the angles and are perpendicular to each other.
3.9.4 Similar Triangle Properties
The document discusses properties of similar triangles that can be used to find unknown segment lengths. It defines 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. It also discusses the triangle angle bisector theorem, where an angle bisector divides the opposite side into segments proportional to the other two sides. Examples are provided to demonstrate using these properties to solve for unknown values.
Understanding quadrilateral
A quadrilateral is a four-sided shape. A parallelogram has each pair of opposite sides parallel. A rhombus is a type of parallelogram with all sides of equal length. A rectangle is a parallelogram with four right angles, and a square is a special type of rectangle where all sides are equal length. A kite has exactly two pairs of equal consecutive sides.
8.4 notes
The document discusses different types of quadrilaterals:
- Parallelograms have both pairs of opposite sides parallel.
- Rhombuses have four equal sides.
- Rectangles have four right angles.
- Squares are both rhombuses and rectangles, with four equal sides and four right angles.
Theorems state that a quadrilateral is a rhombus if its diagonals are perpendicular, or if each diagonal bisects a pair of opposite sides. A quadrilateral is a rectangle if its diagonals are parallel.
Understanding Quadrilaterals Class 8
1. The document defines and classifies different types of polygons, with a focus on quadrilaterals.
2. It describes properties of quadrilaterals including having four sides, four angles, one pair of diagonals, and the interior angle sum being 360 degrees.
3. Several specific types of quadrilaterals are defined, including rectangles, rhombus, squares, parallelograms, trapezoids, kites, and trapeziums. Their defining properties are provided.
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
Gch7 l3
1. The document discusses triangle similarity and the different postulates and theorems used to prove triangles are similar, including AA similarity, SSS similarity, and SAS similarity.
2. Examples are provided to demonstrate using these rules to verify similarity between triangles and find missing side lengths in similar triangles using proportional reasoning. Proofs of triangle similarity are also presented.
3. Applications of triangle similarity include finding dimensions in similar right triangles that model roof designs and solving other geometric problems.
Quadrilateral
A quadrilateral is a polygon with four sides and four vertices. There are different types of quadrilaterals classified by their properties, such as having four equal sides and four right angles (rectangle), four equal sides and two pairs of opposite parallel sides (parallelogram), or two pairs of opposite parallel sides and opposite equal angles (rhombus). The document discusses classifying different quadrilaterals and relating them to everyday life.
Understanding quadrilaterals
A quadrilateral is a 4-sided polygon. There are 5 main types of quadrilaterals: square, rectangle, rhombus, trapezoid, and parallelogram. Each type has distinct properties like the lengths of sides, lengths of angles, lengths of diagonals. A quadrilateral is named based on the order of its vertices.
Similar triangles
The document discusses similar triangles and how to use proportions to solve problems involving similar triangles. It provides examples of setting up proportions between corresponding sides of similar triangles to determine unknown side lengths. It also gives examples of applying similar triangle proportions to solve real-world problems involving shadows.
3.8.4 Triangle Similarity
* Prove certain triangles are similar by using AA~, SSS~, and SAS~
* Use triangle similarity to solve problems.
Saranya a
This document defines and describes different types of quadrilaterals. It states that a quadrilateral is a four-sided closed figure. The main types of quadrilaterals discussed are the parallelogram, rectangle, square, rhombus, trapezium, and isosceles trapezium. Each shape is defined by its geometric properties, such as having parallel sides, equal sides, right angles, and diagonals that bisect each other.
Inequality theorem (l4)
The triangle inequality theorem states that the sum of any two side lengths of a triangle must be greater than the third side length. This means that if you are given two side lengths, you can determine the possible range of values for the third side length. The theorem can also be used to determine if three given side lengths could form a triangle. An example problem shows that sides of lengths 1, 2, and 3 do not form a triangle because 1 + 2 is not greater than 3.
Similarity day 1 sss, sas, aa
The document contains information about using similarity postulates to determine if triangles are similar and find unknown side lengths. It provides examples of using the AA, SAS, and SSS similarity postulates to show triangles are similar. It also shows using proportional sides to find missing lengths. The objective is for students to use similarity postulates to decide if triangles are similar and find unknowns.
Understanding quadrilaterals chapter 3 NCERT
1. The document discusses different types of quadrilaterals including their definitions and properties.
2. Quadrilaterals are classified based on characteristics such as equal side lengths, parallel sides, right angles, and diagonals.
3. The main quadrilaterals discussed are rectangles, rhombus, squares, parallelograms, trapezoids, kites, and general quadrilaterals. Formulas for interior angle sums and relationships between different quadrilaterals are also provided.
Special Quadrilaterals All Of Chapter 8
The document discusses different types of quadrilaterals (four-sided polygons), including their defining properties. It describes parallelograms, rectangles, rhombuses, squares, trapezoids, and kites. Key properties include having parallel sides, right angles, congruent sides, bisected diagonals, and perpendicular or congruent diagonals. A Venn diagram compares the properties of these special quadrilaterals.
Properties of Parallelograms
The document defines and describes the key properties of parallelograms. It states that a parallelogram is a quadrilateral with two pairs of parallel sides. The properties outlined are: the opposite sides of a parallelogram are parallel and equal in length; the opposite angles of a parallelogram are equal; each diagonal of a parallelogram bisects the other; and consecutive angles of a parallelogram are supplementary. The document provides examples for students to practice applying these properties.
7.4 Triangle Proportionality Theorems
This document discusses proportionality theorems in triangles. It defines 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. It also discusses the two transversal proportionality theorem and the triangle angle bisector theorem. Examples are provided to illustrate using these theorems to find unknown side lengths and verify proportions.
Quadrilaterals
The document defines quadrilaterals as polygons with 4 sides and 4 angles. It states that the sum of the interior angles of any quadrilateral is always 360 degrees. It provides an example of using this fact to find the value of an unknown angle. Finally, it lists and defines the different types of quadrilaterals, including general quadrilaterals, trapezoids, parallelograms, rectangles, squares, rhombuses.
Quadrilaterals
This document defines quadrilaterals as polygons with 4 sides and 4 angles. It states that the sum of all interior angles in any quadrilateral is 360 degrees. It then lists and defines the different types of quadrilaterals: trapezium, trapezoid, parallelogram, rectangle, rhombus, and square.
2.8.4 Kites and Trapezoids
This document discusses properties of kites and trapezoids. It defines kites as quadrilaterals with two pairs of congruent consecutive nonparallel sides, and notes their diagonals are perpendicular. It defines trapezoids as quadrilaterals with one pair of parallel sides called bases, and notes angles along the legs are supplementary. It provides theorems about isosceles trapezoids having congruent base angles or congruent diagonals. It also states the midsegment theorem for trapezoids.
8.3 quadrilaterals
- The document discusses classifying triangles and quadrilaterals based on their side lengths and angles. It defines different types of quadrilaterals such as parallelograms, rectangles, rhombuses, trapezoids, and squares.
- Examples are provided for classifying quadrilaterals and finding unknown angle measures using the fact that the sum of interior angles in any quadrilateral is always 360 degrees.
- Students are assigned homework problems involving classifying triangles and quadrilaterals and finding unknown angle measures.
More Related Content
What's hot
5 lesson 3 rectangles, rhombi, and squares
The document lists the key properties of a parallelogram, rectangle, rhombus, and square. A parallelogram has two pairs of parallel sides, while a rectangle has four right angles and opposite sides that are equal. A rhombus has four equal sides and diagonals that bisect the angles. A square has four equal sides and four equal angles, with diagonals that bisect the angles and are perpendicular to each other.
3.9.4 Similar Triangle Properties
The document discusses properties of similar triangles that can be used to find unknown segment lengths. It defines 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. It also discusses the triangle angle bisector theorem, where an angle bisector divides the opposite side into segments proportional to the other two sides. Examples are provided to demonstrate using these properties to solve for unknown values.
Understanding quadrilateral
A quadrilateral is a four-sided shape. A parallelogram has each pair of opposite sides parallel. A rhombus is a type of parallelogram with all sides of equal length. A rectangle is a parallelogram with four right angles, and a square is a special type of rectangle where all sides are equal length. A kite has exactly two pairs of equal consecutive sides.
8.4 notes
The document discusses different types of quadrilaterals:
- Parallelograms have both pairs of opposite sides parallel.
- Rhombuses have four equal sides.
- Rectangles have four right angles.
- Squares are both rhombuses and rectangles, with four equal sides and four right angles.
Theorems state that a quadrilateral is a rhombus if its diagonals are perpendicular, or if each diagonal bisects a pair of opposite sides. A quadrilateral is a rectangle if its diagonals are parallel.
Understanding Quadrilaterals Class 8
1. The document defines and classifies different types of polygons, with a focus on quadrilaterals.
2. It describes properties of quadrilaterals including having four sides, four angles, one pair of diagonals, and the interior angle sum being 360 degrees.
3. Several specific types of quadrilaterals are defined, including rectangles, rhombus, squares, parallelograms, trapezoids, kites, and trapeziums. Their defining properties are provided.
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
Gch7 l3
1. The document discusses triangle similarity and the different postulates and theorems used to prove triangles are similar, including AA similarity, SSS similarity, and SAS similarity.
2. Examples are provided to demonstrate using these rules to verify similarity between triangles and find missing side lengths in similar triangles using proportional reasoning. Proofs of triangle similarity are also presented.
3. Applications of triangle similarity include finding dimensions in similar right triangles that model roof designs and solving other geometric problems.
Quadrilateral
A quadrilateral is a polygon with four sides and four vertices. There are different types of quadrilaterals classified by their properties, such as having four equal sides and four right angles (rectangle), four equal sides and two pairs of opposite parallel sides (parallelogram), or two pairs of opposite parallel sides and opposite equal angles (rhombus). The document discusses classifying different quadrilaterals and relating them to everyday life.
Understanding quadrilaterals
A quadrilateral is a 4-sided polygon. There are 5 main types of quadrilaterals: square, rectangle, rhombus, trapezoid, and parallelogram. Each type has distinct properties like the lengths of sides, lengths of angles, lengths of diagonals. A quadrilateral is named based on the order of its vertices.
Similar triangles
The document discusses similar triangles and how to use proportions to solve problems involving similar triangles. It provides examples of setting up proportions between corresponding sides of similar triangles to determine unknown side lengths. It also gives examples of applying similar triangle proportions to solve real-world problems involving shadows.
3.8.4 Triangle Similarity
* Prove certain triangles are similar by using AA~, SSS~, and SAS~
* Use triangle similarity to solve problems.
Saranya a
This document defines and describes different types of quadrilaterals. It states that a quadrilateral is a four-sided closed figure. The main types of quadrilaterals discussed are the parallelogram, rectangle, square, rhombus, trapezium, and isosceles trapezium. Each shape is defined by its geometric properties, such as having parallel sides, equal sides, right angles, and diagonals that bisect each other.
Inequality theorem (l4)
The triangle inequality theorem states that the sum of any two side lengths of a triangle must be greater than the third side length. This means that if you are given two side lengths, you can determine the possible range of values for the third side length. The theorem can also be used to determine if three given side lengths could form a triangle. An example problem shows that sides of lengths 1, 2, and 3 do not form a triangle because 1 + 2 is not greater than 3.
Similarity day 1 sss, sas, aa
The document contains information about using similarity postulates to determine if triangles are similar and find unknown side lengths. It provides examples of using the AA, SAS, and SSS similarity postulates to show triangles are similar. It also shows using proportional sides to find missing lengths. The objective is for students to use similarity postulates to decide if triangles are similar and find unknowns.
Understanding quadrilaterals chapter 3 NCERT
1. The document discusses different types of quadrilaterals including their definitions and properties.
2. Quadrilaterals are classified based on characteristics such as equal side lengths, parallel sides, right angles, and diagonals.
3. The main quadrilaterals discussed are rectangles, rhombus, squares, parallelograms, trapezoids, kites, and general quadrilaterals. Formulas for interior angle sums and relationships between different quadrilaterals are also provided.
Special Quadrilaterals All Of Chapter 8
The document discusses different types of quadrilaterals (four-sided polygons), including their defining properties. It describes parallelograms, rectangles, rhombuses, squares, trapezoids, and kites. Key properties include having parallel sides, right angles, congruent sides, bisected diagonals, and perpendicular or congruent diagonals. A Venn diagram compares the properties of these special quadrilaterals.
Properties of Parallelograms
The document defines and describes the key properties of parallelograms. It states that a parallelogram is a quadrilateral with two pairs of parallel sides. The properties outlined are: the opposite sides of a parallelogram are parallel and equal in length; the opposite angles of a parallelogram are equal; each diagonal of a parallelogram bisects the other; and consecutive angles of a parallelogram are supplementary. The document provides examples for students to practice applying these properties.
7.4 Triangle Proportionality Theorems
This document discusses proportionality theorems in triangles. It defines 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. It also discusses the two transversal proportionality theorem and the triangle angle bisector theorem. Examples are provided to illustrate using these theorems to find unknown side lengths and verify proportions.
Quadrilaterals
The document defines quadrilaterals as polygons with 4 sides and 4 angles. It states that the sum of the interior angles of any quadrilateral is always 360 degrees. It provides an example of using this fact to find the value of an unknown angle. Finally, it lists and defines the different types of quadrilaterals, including general quadrilaterals, trapezoids, parallelograms, rectangles, squares, rhombuses.
Quadrilaterals
This document defines quadrilaterals as polygons with 4 sides and 4 angles. It states that the sum of all interior angles in any quadrilateral is 360 degrees. It then lists and defines the different types of quadrilaterals: trapezium, trapezoid, parallelogram, rectangle, rhombus, and square.
What's hot (20)
Similar to 8.4 notes
2.8.4 Kites and Trapezoids
This document discusses properties of kites and trapezoids. It defines kites as quadrilaterals with two pairs of congruent consecutive nonparallel sides, and notes their diagonals are perpendicular. It defines trapezoids as quadrilaterals with one pair of parallel sides called bases, and notes angles along the legs are supplementary. It provides theorems about isosceles trapezoids having congruent base angles or congruent diagonals. It also states the midsegment theorem for trapezoids.
8.3 quadrilaterals
- The document discusses classifying triangles and quadrilaterals based on their side lengths and angles. It defines different types of quadrilaterals such as parallelograms, rectangles, rhombuses, trapezoids, and squares.
- Examples are provided for classifying quadrilaterals and finding unknown angle measures using the fact that the sum of interior angles in any quadrilateral is always 360 degrees.
- Students are assigned homework problems involving classifying triangles and quadrilaterals and finding unknown angle measures.
theorems on square.pptx
This document discusses theorems related to squares. It defines a square as a parallelogram with four congruent sides and four right angles. It presents four theorems: 1) if a parallelogram has a right angle, it is a rectangle; 2) the diagonals of a rectangle are congruent; 3) the diagonals of a rhombus are perpendicular; 4) each diagonal of a rhombus bisects the other. It applies these theorems to squares, provides examples of solving problems involving squares, and gives properties and assessment questions about squares.
9.3 Special Parallelograms
Prove and apply properties of special parallelograms.
Use properties of special parallelograms to solve problems
Mathโs assignment quadrilateral
This document discusses properties of quadrilaterals including their areas, diagonals, and special cases. It defines a quadrilateral as a polygon with four sides and vertices. The interior angles of any quadrilateral add up to 360 degrees. Formulas are provided for calculating the area of quadrilaterals in general and some special cases like rectangles where equality is achieved. Properties discussed include how squares maximize area for a given perimeter and orthodiagonal quadrilaterals maximize area for given diagonals. A table compares properties of diagonals for different types of quadrilaterals like whether they bisect, are perpendicular, or are equal length.
2.8.3 Special Parallelograms
This document discusses two special types of parallelograms: rectangles and rhombuses. It provides the key properties of each shape: rectangles have four right angles and diagonals that are congruent, while rhombuses have four congruent sides and perpendicular diagonals that bisect opposite angles. Examples are given to demonstrate using these properties to solve problems, such as finding missing side lengths.
Q2M1-4.pptx
This document discusses different types of quadrilaterals including their definitions and properties. It defines a quadrilateral as a four-sided polygon and introduces various terms used to describe quadrilateral parts such as sides, angles, and diagonals. It then presents different types of quadrilaterals in a family tree showing their relationships and provides detailed definitions and properties for parallelograms, rhombuses, rectangles, and squares. The document concludes with an example problem involving finding measurements of a parallelogram using its properties.
Quadrilaterals
This document defines and describes properties of different types of quadrilaterals. It states that quadrilaterals are four-sided polygons, and defines parallelograms as quadrilaterals with both pairs of opposite sides parallel. Properties of parallelograms include having congruent opposite sides and angles. Rectangles are defined as parallelograms with four right angles, while squares are rectangles with four congruent sides. Rhombuses are parallelograms with four congruent sides. Trapezoids have one pair of parallel sides. Formulas are provided for calculating areas of parallelograms, triangles, trapezoids and other shapes.
Obj. 28 Kites and Trapezoids
1) The document discusses properties of kites and trapezoids, including that kites have perpendicular diagonals and one pair of congruent opposite angles, and trapezoids have one pair of parallel sides called bases.
2) It provides theorems about isosceles trapezoids, including that each pair of base angles is congruent if it is isosceles.
3) The trapezoid midsegment theorem states that the midsegment of a trapezoid is parallel to the bases and its length is half the sum of the base lengths.
presentation1
The document discusses different types of quadrilaterals. It defines a quadrilateral as a polygon with four sides and four vertices. It then describes specific types of quadrilaterals like parallelograms, rectangles, squares, rhombi, kites, trapezoids, and cyclic quadrilaterals. Parallelograms have two pairs of parallel sides, with opposite sides being equal in length and opposite angles being equal. Rectangles are parallelograms with four right angles, while squares are rectangles with all four sides of equal length. The document provides properties and formulas for calculating areas and perimeters of these shapes.
8.4 properties of rhombuses, rectangles, and squares
This document discusses properties of rhombuses, rectangles, and squares. It contains examples of classifying quadrilaterals as rhombuses or rectangles based on given properties. One example asks whether the diagonals of a window opening form a rectangle. The document also includes guided practice problems asking students to determine whether statements are always or sometimes true of certain quadrilaterals or to classify shapes. Key theorems discussed are that opposite angles of parallelograms are congruent, diagonals of rectangles are congruent and bisect each other, and properties used to define rhombuses, rectangles and squares.
Quadrilaterals
This document defines and describes various types of quadrilaterals. It discusses properties such as the angle sum property, and defines specific quadrilaterals like parallelograms, rectangles, squares, rhombi, trapezoids, and kites. It provides theorems regarding properties of parallelograms and how midpoints can be used to prove lines are parallel and halves of other lines. In total, the document comprehensively covers the characteristics and relationships of different quadrilaterals.
Proves theorems on the different kinds of parallelogram.pptx
This document provides information about different types of parallelograms - rectangles, rhombuses, and squares. It defines their key properties and includes theorems about each type. Theorems discussed include: if a parallelogram has a right angle it is a rectangle; the diagonals of a rectangle are congruent; in a rhombus the diagonals are perpendicular and bisect each other; and the diagonals of a square bisect each other, are congruent and perpendicular. Examples are also provided to demonstrate applying the theorems.
Geometry Section 6-5
The document discusses rhombi and squares. It defines a rhombus as a parallelogram with four congruent sides and gives its properties. A square is defined as a parallelogram with four right angles and four congruent sides. The document provides theorems for identifying rhombi and squares. It then gives examples of using the properties and theorems to determine if a shape is a rhombus, rectangle, or square.
Quadrilaterals
This document provides information about various types of quadrilaterals (four-sided shapes). It defines quadrilateral, rectangle, rhombus, square, parallelogram, and trapezium. For each shape, it describes the key properties like side lengths, angle measures, and how to calculate the area and perimeter. The goal is to explain these geometric concepts in a clear, step-by-step manner to make mathematics more accessible and enjoyable for students.
Introduction of Quadrilaterals
This document introduces different types of quadrilaterals. It defines a quadrilateral as a 2D shape with four straight sides. The main types discussed are rectangles, rhombi, squares, parallelograms, trapezoids, kites, and irregular quadrilaterals. It provides characteristics to define each type, such as sides of equal length or right angles. Additionally, it presents a family tree showing how some quadrilaterals are subsets of others, like squares being a type of rectangle. In conclusion, the document establishes the foundation for understanding different quadrilateral categories.
2.8.5 Kites and Trapezoids
This document discusses properties of kites and trapezoids. It defines kites as quadrilaterals with two pairs of congruent consecutive sides and states properties of kites including perpendicular diagonals and one pair of opposite congruent angles. It also defines trapezoids as quadrilaterals with one pair of parallel sides, called bases, and discusses isosceles trapezoids. Theorems are presented about base angles and diagonals of isosceles trapezoids. The midsegment theorem for trapezoids states the midsegment is parallel to the bases and its length is half the sum of the base lengths. Examples apply the properties and theorems to solve problems.
Geom 6point4 97
This document defines and compares rhombuses, rectangles, and squares. It states that a rhombus is a parallelogram with four congruent sides, a rectangle is a parallelogram with four right angles, and a square is a parallelogram that is both a rhombus and a rectangle. The document also presents properties and relationships between these shapes, such as diagonals and angles, and provides theorems about identifying shapes based on their diagonals.
Quadrilaterals project
The document defines properties and methods to prove different types of quadrilaterals. It discusses properties and proofs for parallelograms, rectangles, kites, rhombuses, squares, and isosceles trapezoids. Key properties include opposite sides being parallel and congruent for parallelograms, right angles for rectangles, perpendicular diagonals for kites, and congruent angles and sides for squares. Methods of proof involve showing opposite sides are parallel/congruent, diagonals bisect each other, or angles are right or congruent.
Day 2 quadrilaterals
This document provides information about different types of quadrilaterals:
1. It defines different types of quadrilaterals including parallelograms, trapezoids, rhombuses, rectangles, and squares.
2. It includes diagrams labeling the characteristics of each shape and flow charts to help identify different quadrilaterals based on their properties.
3. Examples are provided to practice identifying and classifying quadrilaterals based on whether they have parallel sides, right angles, or congruent sides. Statements about quadrilaterals are also identified as true or false.
Similar to 8.4 notes (20)
8.4 properties of rhombuses, rectangles, and squares
8.4 properties of rhombuses, rectangles, and squares
ย
Proves theorems on the different kinds of parallelogram.pptx
Proves theorems on the different kinds of parallelogram.pptx
ย
More from Mrs. Hedrick's Class
Strafford Volleyball Apparel
This document appears to be an order form for Strafford Indian Volleyball apparel and merchandise. It lists various items available for purchase including short sleeve t-shirts, long sleeve t-shirts, hoodies, wind shirts, shorts, track jackets, hats, and more. The items are available in a range of sizes from youth to adult sizes. Each item lists a price and there are options for different embroidery designs on some of the jackets and hats.
Ch 12 unit schedule
This document outlines the Geometry 2016 Chapter 12 unit on 3D shapes that will be covered from April 11th to April 29th. It includes the chapter sections and topics to be covered each day, such as different types of prisms and pyramids, as well as the homework assignments and assessments including quizzes, tests, and a study guide.
Ch 10 unit schedule
This document provides a schedule for Geometry Chapter 10 on Circles over a two week period from February 29th to March 11th and March 21st to March 25th. Each day covers a different section of the chapter, with assigned problems and quizzes listed. The schedule culminates with a paper plate review, studying for the chapter test, taking the test, and then correcting any errors on the test.
Ch 7 unit schedule
This document outlines the Geometry unit 7 schedule for January 2016. It includes lessons on sections 7.1 through 7.4 focusing on trigonometry, with worksheets and quizzes planned for most days. A practice quiz, study guide, and trigonometry test are scheduled for the third week. Snow days are noted on January 15th and 18th, with tutoring available by arrangement.
Stockton Tournament Schedule 2015
The document summarizes a volleyball tournament taking place on October 3, 2015 in Stockton. It outlines the tournament structure, including three pools (A, B, C) divided by age/skill level with 4 teams each. A schedule is provided for round robin pool play matches between the teams, with the top two teams from each pool and the next two best records advancing to bracket playoff rounds. Bracket play will begin at 1:30 PM and be a best-of-three format to determine 1st, 2nd, and 3rd place trophies.
Lake Volley Fest
The JV Lake Volley Fest 2015 volleyball tournament will take place on September 26th. Seven teams will be split into the Purple Pool and Gold Pool, with the top two teams from each pool advancing to the Championship Bracket and the bottom two advancing to the Consolation Bracket. The tournament schedule lists the matchups for each of the six time slots between 8:30am and 12:15pm across the two courts. Plaques will be awarded to the first and second place finishers.
Lake Volley Fest
Camdenton High School will host the 2015 Lake Volley Fest Tournament on September 26th. There will be two courts located on campus for pool play and bracket play. Teams will be responsible for providing their own line judge. The top four teams will advance to the championship bracket, while the bottom four teams will play in the consolation bracket. Plaques will be awarded to the first and second place finishers.
Volleyfest Schedule 2015
This document contains the schedule for the 19th Annual Strafford Volleyfest volleyball tournament held on September 19, 2015. It lists the three courts where matches will take place and provides the schedule of games for each court, with start times ranging from 8:30 AM to 6:15 PM. It identifies the 12 participating schools that are divided into three pools based on color. It explains that after pool play, the top six teams will advance to the Championship Bracket and the bottom six to the Consolation Bracket for playoff matches.
2015 Branson Tournament Schedule
The document provides information about the 2015 Branson Invitational volleyball tournament including pool and bracket structures. Sixteen teams will be divided into four pools of four teams each to play a round robin. Pool play will consist of best-of-three sets and teams will be ranked 1-16 based on win-loss record, point differential, and head-to-head results. The top eight teams will advance to the gold bracket and bottom eight to the silver bracket for single elimination bracket play consisting of best-of-three sets.
12.7 notes
This document contains notes from a math class on similar solids. It defines similar solids as two solids of the same type that have equal ratios, known as a scale factor. It then states the Similar Solids Theorem: if two similar solids have a scale factor of a:b, their corresponding areas have a ratio of a2:b2 and their corresponding volumes have a ratio of a3:b3. Examples of homework problems involving similar solids are listed.
12.6 notes
The document discusses surface area and volume formulas for spheres. It provides examples of calculating the surface area of spheres with given diameters, as well as the volume of spheres and other objects like snow cones that can be modeled as spheres. Students are assigned homework problems applying these formulas to calculate surface areas and volumes.
12.5 notes
The document is notes from a math class lesson on finding the volumes of cones and pyramids. It includes the objectives of learning the formulas for these volumes. The formulas given are that the volume of a cone is 1/3ฯr^2h and the volume of a pyramid is 1/3Bh, where B is the area of the base and h is the height. There are examples provided of applying these formulas to find volumes.
12.4 notes
This document contains notes from a math lesson on finding the volumes of prisms and cylinders. It defines volume as the amount of space inside an object. It explains that to find the volume of a prism or cylinder, you calculate the area of the base and multiply it by the height. For a prism, the base can be any shape and its area formula is used. For a cylinder, the base is a circle so the volume formula is ฯr^2h, with r as the radius and h as the height. Examples of volume problems are shown and homework problems are assigned from the textbook.
Indian volleyball tournament
A volleyball tournament will be held on May 2nd at 9am at the Max Evans Gym to benefit the Strafford Indian Volleyball Program. The tournament will feature fun rules, games and prizes and cost $10 per person to register, either as part of a team of 6-8 players or individually. People can register their teams on Facebook or by contacting the coaches Ashley Bough or Angelina Hedrick by May 1st.
12.3 notes
This document contains notes and examples for calculating the surface area of pyramids and cones. It provides the formulas for finding the surface area of regular pyramids and cones. For pyramids, the surface area equals one-half the perimeter of the base times the sum of the slant height and apothem. For cones, the surface area equals pi times the radius squared plus pi times the radius times the slant height. The document includes practice problems applying these formulas to find the surface area of various pyramids and cones.
12.2 notes
The document discusses surface area formulas for prisms and cylinders. It defines surface area as the sum of the areas of all surfaces that enclose a solid. For prisms, surface area is calculated as the perimeter of the base multiplied by the height, plus twice the area of the base. For cylinders, surface area is the circumference of the base multiplied by the height, plus twice the area of the circular base. The document provides examples of applying these formulas to prisms and cylinders.
12.5 notes
This document contains information about the law of cosines from a geometry homework assignment on page 678 problems 14 through 20, dated April 09, 2015. The document title and date are repeated multiple times.
12.4 notes
This document contains information about the law of sines for a math homework assignment. It lists the topic as the law of sines and directs the student to problems 15-17 and 29-31 on page 672 of their homework, which was assigned on April 08, 2015. The document repeats this information four times.
12.1 notes
This document contains notes from a math class where students were working on homework problems involving trigonometry (SOHCAHTOA) and multiples of 3. The notes are dated April 08, 2015 and reference homework page 648 problems 12 through 36 dealing with multiples of 3.
11.7 notes
This document contains notes from an 11th grade math class on the topic of geometric probability. It includes examples of calculating the probability of events based on ratios of lengths and areas, such as the probability of a driver speeding in front of a school based on the length of road in front of the school over the total road length. The homework problems assigned were problems 4-10 of the even numbers, 20-23, and 30-33 on page 774 of the textbook.
More from Mrs. Hedrick's Class (20)
Recently uploaded
How to Download & Install Module From the Odoo App Store in Odoo 17
Custom modules offer the flexibility to extend Odoo's capabilities, address unique requirements, and optimize workflows to align seamlessly with your organization's processes. By leveraging custom modules, businesses can unlock greater efficiency, productivity, and innovation, empowering them to stay competitive in today's dynamic market landscape. In this tutorial, we'll guide you step by step on how to easily download and install modules from the Odoo App Store.
BIOLOGY NATIONAL EXAMINATION COUNCIL (NECO) 2024 PRACTICAL MANUAL.pptx
Practical manual for National Examination Council, Nigeria.
Contains guides on answering questions on the specimens provided
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
The recent surge in pro-Palestine student activism has prompted significant responses from universities, ranging from negotiations and divestment commitments to increased transparency about investments in companies supporting the war on Gaza. This activism has led to the cessation of student encampments but also highlighted the substantial sacrifices made by students, including academic disruptions and personal risks. The primary drivers of these protests are poor university administration, lack of transparency, and inadequate communication between officials and students. This study examines the profound emotional, psychological, and professional impacts on students engaged in pro-Palestine protests, focusing on Generation Z's (Gen-Z) activism dynamics. This paper explores the significant sacrifices made by these students and even the professors supporting the pro-Palestine movement, with a focus on recent global movements. Through an in-depth analysis of printed and electronic media, the study examines the impacts of these sacrifices on the academic and personal lives of those involved. The paper highlights examples from various universities, demonstrating student activism's long-term and short-term effects, including disciplinary actions, social backlash, and career implications. The researchers also explore the broader implications of student sacrifices. The findings reveal that these sacrifices are driven by a profound commitment to justice and human rights, and are influenced by the increasing availability of information, peer interactions, and personal convictions. The study also discusses the broader implications of this activism, comparing it to historical precedents and assessing its potential to influence policy and public opinion. The emotional and psychological toll on student activists is significant, but their sense of purpose and community support mitigates some of these challenges. However, the researchers call for acknowledging the broader Impact of these sacrifices on the future global movement of FreePalestine.
skeleton System.pdf (skeleton system wow)
๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ
โ โุฅุถุบ ุจูู ุฅูุฏููู
โู
ู ุฃููู ุงูู
ูุงุฒู
ุงูุชู ุตู
ู
ุชูุง
ู
ูุฒู
ุฉ ุชุดุฑูุญ ุงูุฌูุงุฒ ุงูููููู (ูุธุฑู 3)
๐๐๐๐๐๐๐๐๐๐
ุชุชู
ูุฒ ูุฐูู ุงูู
ูุฒู
ุฉ ุจุนูุฏุฉ ู
ูู
ูุฒุงุช :
1- ู
ูุชุฑุฌู
ุฉ ุชุฑุฌู
ุฉ ุชููุงุณุจ ุฌู
ูุน ุงูู
ุณุชููุงุช
2- ุชุญุชูู ุนูู 78 ุฑุณู
ุชูุถูุญู ููู ููู
ุฉ ู
ูุฌูุฏุฉ ุจุงูู
ูุฒู
ุฉ (ููู ููู
ุฉ !!!!)
#ููู
_ู
ุงูู_ุฏุฑุฎ
3- ุฏูุฉ ุงููุชุงุจุฉ ูุงูุตูุฑ ุนุงููุฉ ุฌุฏุงู ุฌุฏุงู ุฌุฏุงู
4- ูููุงูู ุจุนุถ ุงูู
ุนููู
ุงุช ุชู
ุชูุถูุญูุง ุจุดูู ุชูุตููู ุฌุฏุงู (ุชูุนุชุจุฑ ูุฏู ุงูุทุงูุจ ุฃู ุงูุทุงูุจุฉ ุจุฅููุง ู
ุนููู
ุงุช ู
ูุจูู
ุฉ ูู
ุน ุฐูู ุชู
ุชูุถูุญ ูุฐูู ุงูู
ุนููู
ุงุช ุงูู
ูุจูู
ุฉ ุจุดูู ุชูุตููู ุฌุฏุงู
5- ุงูู
ูุฒู
ุฉ ุชุดุฑุญ ููุณูุง ุจ ููุณูุง ุจุณ ุชููู ุชุนุงู ุงูุฑุงูู
6- ุชุญุชูู ุงูู
ูุฒู
ุฉ ูู ุงูู ุณูุงูุฏ ุนูู ุฎุงุฑุทุฉ ุชุชุถู
ู ุฌู
ูุน ุชูุฑูุนุงุช ู
ุนููู
ุงุช ุงูุฌูุงุฒ ุงูููููู ุงูู
ุฐููุฑุฉ ูู ูุฐูู ุงูู
ูุฒู
ุฉ
ูุงุฎูุฑุงู ูุฐูู ุงูู
ูุฒู
ุฉ ุญูุงูู ุนูููู
ูุฅุชู
ูู ู
ููู
ุฅู ุชุฏุนููู ุจุงูุฎูุฑ ูุงูุตุญุฉ ูุงูุนุงููุฉ ููุท
ูู ุงูุชูููู ุฒู
ูุงุฆู ูุฒู
ููุงุชู ุ ุฒู
ูููู
ู
ุญู
ุฏ ุงูุฐูุจู ๐๐
๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ
CapTechTalks Webinar Slides June 2024 Donovan Wright.pptx
Slides from a Capitol Technology University webinar held June 20, 2024. The webinar featured Dr. Donovan Wright, presenting on the Department of Defense Digital Transformation.
Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...
Andreas Schleicher, Director of Education and Skills at the OECD presents at the launch of PISA 2022 Volume III - Creative Minds, Creative Schools on 18 June 2024.
BPSC-105 important questions for june term end exam
BPSC-105 important questions for june term end exam
Accounting for Restricted Grants When and How To Record Properly
In this webinar, member learned how to stay in compliance with generally accepted accounting principles (GAAP) for restricted grants.
BรI TแบฌP Bแป TRแปข TIแบพNG ANH LแปP 8 - Cแบข NฤM - FRIENDS PLUS - NฤM HแปC 2023-2024 (B...
BรI TแบฌP Bแป TRแปข TIแบพNG ANH LแปP 8 - Cแบข NฤM - FRIENDS PLUS - NฤM HแปC 2023-2024 (B...Nguyen Thanh Tu Collection
https://app.box.com/s/nrwz52lilmrw6m5kqeqn83q6vbdp8yzpย
ู
ุตุญู ุงููุฑุงุกุงุช ุงูุนุดุฑ ุฃุนุฏ ุฃุญุฑู ุงูุฎูุงู ุณู
ูุฑ ุจุณูููู.pdf
ู
ุตุญู ุงููุฑุงุกุงุช ุงูุนุดุฑ ุฃุนุฏ ุฃุญุฑู ุงูุฎูุงู ุณู
ูุฑ ุจุณูููู.pdfุณู
ูุฑ ุจุณูููู
ู
ุตุญู ุฃุญุฑู ุงูุฎูุงู ูููุฑุงุก ุงูุนุดุฑุฉุฃุนุฏ ุฃุญุฑู ุงูุฎูุงู ุจุงูุชูููู ูุตูุง ุณู
ูุฑ ุจุณูููู ุบูุฑ ุงููู ููย
How to Manage Reception Report in Odoo 17
A business may deal with both sales and purchases occasionally. They buy things from vendors and then sell them to their customers. Such dealings can be confusing at times. Because multiple clients may inquire about the same product at the same time, after purchasing those products, customers must be assigned to them. Odoo has a tool called Reception Report that can be used to complete this assignment. By enabling this, a reception report comes automatically after confirming a receipt, from which we can assign products to orders.
How to Fix [Errno 98] address already in use
This slide will represent the cause of the error โ[Errno 98] address already in useโ and the troubleshooting steps to resolve this error in Odoo.
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) Curriculum
(๐๐๐ ๐๐๐) (๐๐๐ฌ๐ฌ๐จ๐ง ๐)-๐๐ซ๐๐ฅ๐ข๐ฆ๐ฌ
๐๐ข๐ฌ๐๐ฎ๐ฌ๐ฌ ๐ญ๐ก๐ ๐๐๐ ๐๐ฎ๐ซ๐ซ๐ข๐๐ฎ๐ฅ๐ฎ๐ฆ ๐ข๐ง ๐ญ๐ก๐ ๐๐ก๐ข๐ฅ๐ข๐ฉ๐ฉ๐ข๐ง๐๐ฌ:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
๐๐ฑ๐ฉ๐ฅ๐๐ข๐ง ๐ญ๐ก๐ ๐๐๐ญ๐ฎ๐ซ๐ ๐๐ง๐ ๐๐๐จ๐ฉ๐ ๐จ๐ ๐๐ง ๐๐ง๐ญ๐ซ๐๐ฉ๐ซ๐๐ง๐๐ฎ๐ซ:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
Recently uploaded (20)
How to Download & Install Module From the Odoo App Store in Odoo 17
How to Download & Install Module From the Odoo App Store in Odoo 17
ย
BIOLOGY NATIONAL EXAMINATION COUNCIL (NECO) 2024 PRACTICAL MANUAL.pptx
BIOLOGY NATIONAL EXAMINATION COUNCIL (NECO) 2024 PRACTICAL MANUAL.pptx
ย
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
ย
CapTechTalks Webinar Slides June 2024 Donovan Wright.pptx
CapTechTalks Webinar Slides June 2024 Donovan Wright.pptx
ย
Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...
Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...
ย
BPSC-105 important questions for june term end exam
BPSC-105 important questions for june term end exam
ย
Accounting for Restricted Grants When and How To Record Properly
Accounting for Restricted Grants When and How To Record Properly
ย
BรI TแบฌP Bแป TRแปข TIแบพNG ANH LแปP 8 - Cแบข NฤM - FRIENDS PLUS - NฤM HแปC 2023-2024 (B...
BรI TแบฌP Bแป TRแปข TIแบพNG ANH LแปP 8 - Cแบข NฤM - FRIENDS PLUS - NฤM HแปC 2023-2024 (B...
ย
ู
ุตุญู ุงููุฑุงุกุงุช ุงูุนุดุฑ ุฃุนุฏ ุฃุญุฑู ุงูุฎูุงู ุณู
ูุฑ ุจุณูููู.pdf
ู
ุตุญู ุงููุฑุงุกุงุช ุงูุนุดุฑ ุฃุนุฏ ุฃุญุฑู ุงูุฎูุงู ุณู
ูุฑ ุจุณูููู.pdf
ย
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) Curriculum
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) Curriculum
ย
Juneteenth Freedom Day 2024 David Douglas School District
Juneteenth Freedom Day 2024 David Douglas School District
ย
8.4 notes
- 1. Tell how you know that the quadrilateral is a parallelogram. 1.The diagonals bisect each other. 2. Both pairs of opp <s โ โด opp sides //. Def of //ogram 3. For what value of x is the quadrilateral a parallelogram? 50 Bellwork 80 10080 2x x + 30
- 2. 8.4 Special Quadrilaterals Rhombus: w/ 4 โ sides Rectangle: w/ 4 right <s Square: w/ 4 sides โ & 4 right <s Rhombus Corollary: A quad is a rhombus iff it has 4 โ sides. Rectangle Corollary: A quad is a rectangle iff it has 4 right <s. Square Corollary: A quad is a square iff it is a rhombus and rectangle. Parallelograms Rhombuses Squares Rectangles
- 5. A is a rhombus iff its diagonals are . A is a rhombus iff each diagonal bisects a pair of opposite <s. A is a rectangle iff its diagonals are โ . Theorem 8.11 Theorem 8.12 Theorem 8.13
- 6. A is a rhombus iff its diagonals are . Theorem 8.11 Rewrite the theorem as a biconditional and prove it. If the diagonals of a are , then it is a rhombus. If the is a rhombus, then its diagonals are . Conditional Statement Converse Given: ABCD is a ; AC BD Prove: ABCD is a rhombus. A CD B X PROOF: Statements Reasons ABCD is a //ogram Given AC BD Given <CXB & <DXC are right <s Def of lines <CXB โ <DXC Def of right <s DX โ BX Diagonals bisect each other in Questions to ask. What do I know about //ograms? What do I know about rhombuses? CX โ XC Reflexive Prop. BXC โ DXC SAS 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 1. 2. 3. 4. 5. 7. 8. 9. 10. 11. 6. BC โ DC CPCTC AD โ BC & DC โ AB Opp. sides of are โ AD โ DC & BC โ AB Transitive Prop. Def of rhombus ABCD is a rhombus
- 8. 8.4 HW pg. 537 #3-51 multiples of 3