1. 6.5 Rhombi and Squares

2. Rhombus
Quad with 4  sides

3. Rhombus Theorem 6.15: The diagonals of a rhombus are  .
Theorem 6.16: If the diagonals of a parallelogram are , then the parallelogram is a rhombus.
Theorem 6.17: Each diagonal of a rhombus bisects a pair of opposite angles.
All 4 of the s are .

4. Example Refer to Example #2 picture on page 349
Do Check Your Progress #2
Answer:
114

5. Square Both a rhombus and a rectangle All sides are 
All angles are right angles (90°)

6. Quadrilaterals
Parallelograms
Rectangles
Rhombi
Squares

7. Example
Given the vertices 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.
Use the distance formula to compare the lengths of the diagonals. Use the slope formula to determine if the sides are perpendicular.
Answer: Square, rectangle, and rhombus, all sides are congruent and perpendicular.

8. Summaries Rhombus Properties Square Properties Opposites sides are 
Opposite angles are 
Consecutive angles are supplementary.
Diagonals bisect each other
Diagonals are perpendicular
Each diagonal bisects two angles.
4 sides are 
Square Properties
Opposites sides are 
Opposite angles are 
Consecutive angles are supplementary.
Diagonals bisect each other
Diagonals are perpendicular
Each diagonal bisects two angles.
All four angles are right angles.
Diagonals are 
4 sides are 

9. Homework #41
p , 15-18, odd, 31-34