5.10 Properties of Rhombuses, Rectangles, and Squares

Slides:

Advertisements

Similar presentations

6.4 Rhombuses, Rectangles, and Squares

Advertisements

6.3/4 Rhombuses, Rectangles, and Squares. Three Definitions 1.A rhombus is a parallelogram with four congruent sides. 1.A rectangle is a parallelogram.

Parallelogram A quadrilateral with both pairs of opposite sides parallel *opposite sides are congruent *opposite angles are congruent *diagonals bisect.

1. Name the five properties of a parallelogram. ANSWER

6.4: Properties of Rhombuses, Rectangles, and Squares

Warm-up Pg 520 #39, 40 Pg 529 # Properties of Rhombuses, Rectangles, and Squares 8.4.

EXAMPLE 1 Use properties of special quadrilaterals

Properties of Rhombuses, Rectangles, & Squares Goal: Use properties of rhombuses, rectangles, & squares.

Prop. of Rhom., Rect., and Squares

Chapter 8.4 Notes: Properties of Rhombuses, Rectangles, and Squares

5.12Identify Special Quadrilaterals Example 1 Identify quadrilaterals Quadrilateral ABCD has both pairs of opposite sides congruent. What types of quadrilaterals.

5.10 Properties of Rhombuses, Rectangles, and Squares

Properties of Quadrilaterals

For each, attempt to create a counter example or find the shape is MUST be….. Quadrilateral Properties.

6.4 Rhombuses, Rectangles, and Squares Day 4 Review  Find the value of the variables. 52° 68° h p (2p-14)° 50° 52° + 68° + h = 180° 120° + h = 180 °

6.4 Properties of Rhombuses, Rectangles, and Squares A rhombus is a parallelogram with four congruent sides. A rectangle is a parallelogram with four right.

5.4 Special Quadrilaterals

Parallelograms have Properties Click to view What is a parallelogram? A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

6.4 Rhombuses, Rectangles and Squares Unit 1C3 Day 5.

Rhombuses, Rectangles, and Squares

Special Parallelograms

Geometry 6-4 Properties of Rhombuses, Rectangles, and Squares.

6-4 Properties of Rhombuses, Rectangles, and Squares

EXAMPLE 3 List properties of special parallelograms

6-4 Properties of Rhombuses, Rectangles, and Squares

Properties of Rhombuses, Rectangles, and Squares Lesson 8.4.

A D B C Definition: Opposite Sides are parallel.

Geometry Section 8.4 Properties of Rhombuses, Rectangles, and Squares.

1. Give five ways to prove that a quadrilateral is a parallelogram.

7.4 Properties of Special Parallelograms OBJ: Students will be able to use properties of special parallelograms and diagonals of special parallelograms.

 6.3 Showing Quadrilaterals are Parallelograms. We can use the theorems from 6.2 to prove that quadrilaterals are parallelograms  What 5 facts are ALWAYS.

A rhombus is a parallelogram with __ ________________ ___________. A rectangle is a parallelogram with ___ __________ ____________. A square is a parallelogram.

Warm Up:  Solve for x and y in the following parallelogram. What properties of parallelograms did you use when solving?  What is the measure of CD? 

6.4 EQ: What properties do we use to identify special types of parallelograms?

Do Now: List all you know about the following parallelograms.

1. Give five ways to prove that a quadrilateral is a parallelogram.

Parallelograms have Properties

Unit 2 – Similarity, Congruence, and Proofs

Rhombus – a quadrilateral with ______ _________ _________ ________

Section 8.4 Notes.

8.4 Properties of Rhombuses, Rectangles, and Squares

EXAMPLE 1 Use properties of special quadrilaterals

Special Quadrilaterals

| | A rhombus is a parallelogram with four congruent sides.

6.4 Rhombi, Rectangles, and Squares

6-4 Properties of Rhombuses, Rectangles, and Squares

6.4 Rhombuses, Rectangles and Squares

Rhombuses, Rectangles, and Squares

Rhombuses, Rectangles, and Squares

Warm Up 1. Date: 2/27/12 Factor the expression by finding the greatest common factor (GCF). y= 3x2 +18x +45 y = 3(x2 +6x +15)

Lesson 6-4: Rhombus & Square

| | A rhombus is a parallelogram with four congruent sides.

Lecture 6-4 Rhombi and Squares.

Section 6.4 rhombuses, rectangles and squares

6-5 Conditions for Rhombuses, Rectangles, and Squares

8.4 Properties of Rhombuses, Rectangles, and Squares

Properties of Special Parallelograms

Properties of Rhombuses, Rectangles, & Squares

8-5: Rhombi and Squares.

Lesson 6-4: Rhombus & Square

What is a quadrilateral??

Prop. of Rhom., Rect., and Squares

Identify Special Quadrilaterals

Lesson 6-4: Rhombus & Square

Solutions to Check point 8.1

Section 6.4 Properties of Rhombi, Rectangles, & Squares

6.4 Rhombuses, Rectangles and Squares

6-4 Squares and Rhombi Objectives:

Go over the Test.

Presentation transcript:

5.10 Properties of Rhombuses, Rectangles, and Squares

Vocabulary A rhombus is a parallelogram with four congruent sides. A rectangle is a parallelogram with four right angles. A square is a parallelogram with four congruent sides and four right angles.

Corollaries Rhombus Corollary: A quadrilateral is a rhombus if and only if it has four congruent sides. Rectangle Corollary: A quadrilateral is a rectangle if and only if it has four right angles. Square Corollary: A quadrilateral is a square if and only if it is a rhombus and a rectangle.

ABCD is a rhombus. ABCD is a rectangle. ABCD is a square.

EXAMPLE 1 Use properties of special quadrilaterals For any rhombus QRST, decide whether the statement is always or sometimes true. Draw a sketch and explain your reasoning. a. Q S SOLUTION a. By definition, a rhombus is a parallelogram with four congruent sides. By Theorem 8.4, opposite angles of a parallelogram are congruent. So, .The statement is always true. Q S

EXAMPLE 1 Use properties of special quadrilaterals For any rhombus QRST, decide whether the statement is always or sometimes true. Draw a sketch and explain your reasoning. Q R b. SOLUTION If rhombus QRST is a square, then all four angles are congruent right angles. So, if QRST is a square. Because not all rhombuses are also squares, the statement is sometimes true. Q R

Theorem 5.26: A parallelogram is a rhombus if and only if its diagonals are perpendicular. Theorem 5.27: A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles. Theorem 5.28: A parallelogram is a rectangle if and only if its diagonals are congruent.