8.4 Properties of Rhombuses, Rectangles, and Squares Hubarth Geometry

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.

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

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

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.

Theorem 8.11 A B D C

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

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

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.

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