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

2. Section 6-5 Rhombi and Squares

3. 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.

4. 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

5. Rhombus: a parallelogram with all four sides congruent.
Vocabulary

6. 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.

7. 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

8. 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

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

11. 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

12. 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

13. 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

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