1. 8.4 Properties of Rhombuses, Rectangles, and Squares
Hubarth
Geometry

2. 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.

3. Ex 1. Use Properties of Special ParallelogramsB
In the diagram, ABCD is a rectangle . 5 D C 8
Solution

4. Corollaries
Rhombus Corollary B A C D
Rectangle Corollary A B C D
Square Corollary

5. Ex 2. Identify Special Quadrilaterals
Use the information in the diagram to name the special quadrilateral. 3 5
Solution
The quadrilateral has four right angles, but does not have four congruent sides.
So, the quadrilateral is a rectangle.

6. Theorem 8.11 A B D C

7. Ex 3. Use Diagonals of a Rhombus
ABCD is a rhombus.
Find the value of x. A B 60 X E D C
Solution

8. Theorem 8.12
A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles
Theorem 8.13 A B D C

9. Ex 4. Use Diagonals of a Rectangle
You nail four pieces of wood together to build a four-sided frame, as shown.
What is the shape of the frame?
b. The diagonals measure 7ft. 4 in. and 7 ft 2 in. Is the frame a rectangle? 4 6 6 4
Solution
a. The frame is a parallelogram because both pairs of opposite sides are congruent.
b. The frame is not a rectangle because the diagonals are not congruent.

10. Practice S 7 R T U
2. Use the information in the diagram to name the quadrilateral. 14
Square 14 14 M 14
3. JKLM is a rhombus. Find the value of x. J T 50
x= 40 L x K
4. ABCD is a rectangle. Find the value of x. A B 10
x=10 x C D