Quadrilateral ABCD is a rectangle Quadrilateral ABCD is a rectangle. If DE = 6x – 7 and AE = 4x + 9, find DB. Problem of the Day

Section 6-5 Rhombi and Squares

Then Now Objectives You determined whether quadrilaterals were parallelograms and/or rectangles. Recognize and apply properties of rhombi and squares. Determine whether quadrilaterals are rectangles, rhombi, and squares.

Common Core State Standards Content Standards G.CO.11 – Prove theorems about parallelograms. G.GPE.4 – Use coordinates to prove simple geometric theorems algebraically. Mathematical Practices 2) Reason abstractly and quantitatively. 3) Construct viable arguments and critique the reasoning of others. Common Core State Standards

Rhombus: a parallelogram with all four sides congruent. Vocabulary

If a parallelogram is a rhombus, then its diagonals are perpendicular. Diagonals of a Rhombus If a parallelogram is a rhombus, then its diagonals are perpendicular. If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles.

Quadrilateral ABCD is a rhombus. Find each value or measure Quadrilateral ABCD is a rhombus. Find each value or measure. a) m∠CEB b) If m∠CBD is 58, find m∠EAD. c) If AD = 2x + 4 and CD = 4x – 4, find x. Example 1

Quadrilateral ABCD is a rhombus. Find each value or measure Quadrilateral ABCD is a rhombus. Find each value or measure. a) If m∠CED is 5x, find x. b) If m∠EAD is 53, find m∠CBE. c) If BC = 8x – 5 and AB = 6x + 3, find x. Example 1

Square: a parallelogram with four congruent sides and four right angles. *A square is both a rectangle and a rhombus! Vocabulary

Given J(5, 0), K(8, -11), L(-3, -14), M(-6, -3), determine whether parallelogram JKLM is a rhombus, a rectangle, or a square. List all that apply. Example 4

Given A(-2, -2), B(-3, 1), C(3, 3), D(4, 0), determine whether parallelogram ABCD is a rhombus, a rectangle, or a square. List all that apply. Example 4

Given E(-4, -1), F(1, -1), G(4, 3), H(-1, 3), determine whether parallelogram EFGH is a rhombus, a rectangle, or a square. List all that apply. Example 4

p.435 #1, 2, 7 – 12, 20, 22, 25, 26 Homework