1. 6.4
EQ: What properties do we use to identify special types of parallelograms?

2. Parallelogram (review)
Both pairs of opposite sides are parallel
Both pairs of opposite sides are congruent
Both pairs of opposite angles are congruent
Consecutive angles are supplementary
Diagonals bisect each other

3. rhombus
a parallelogram with four congruent sides.

4. rhombus
a parallelogram with four congruent sides.

5. rectangle
A parallelogram with four right angles.

6. rectangle
A parallelogram with four right angles.

7. rectangle
A parallelogram with four right angles.

8. square
A parallelogram with four congruent sides and four right angles.

9. square
A parallelogram with four congruent sides and four right angles.

10. AD = BC = 5 and AB = DC = 8. Example 1
Use Properties of Special Parallelograms
In the diagram, ABCD is a rectangle. b.
Find mA, mB, mC, and mD.
Find AD and AB. a.
SOLUTION
AD = BC = 5 and AB = DC = 8. a.
By definition, a rectangle has four right angles, so mA = mB = mC = mD = 90°. b.

11. QR = 6, RS = 6, SP = 6 Checkpoint In the diagram, PQRS is a rhombus.
Use Properties of Special Parallelograms
In the diagram, PQRS is a rhombus.
Find QR, RS, and SP. 1.
ANSWER
QR = 6, RS = 6, SP = 6

12. Rhombus Corollary
If a quadrilateral has four congruent sides, then it is a rhombus.

13. Rectangle Corollary
If a quadrilateral has four right angles, then it is a rectangle.

14. Square Corollary
If a quadrilateral has four congruent sides and four right angles, then it is a square.

15. Use the information in the diagram to name the special quadrilateral.
Checkpoint
Identify Special Quadrilaterals
Use the information in the diagram to name the special quadrilateral. 2.
ANSWER
rhombus 3.
ANSWER
square 15

16. The diagonals of a rhombus are perpendicular.
Theorem 6.10

17. Example 3
Use Diagonals of a Rhombus
ABCD is a rhombus. Find the value of x.
SOLUTION
So, x = 90 – 60 = 30. 17

18. Theorem 6.11
The diagonals of a rectangle are congruent.

19. Checkpoint Find the value of x. rhombus ABCD 4. ANSWER 90
Use Diagonals
Find the value of x.
rhombus ABCD 4.
ANSWER 90
rectangle EFGH 5.
ANSWER 12
square JKLM 6.
ANSWER 45 19