Properties of Special Parallelograms

Properties of Special Parallelograms 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. parallelograms rhombuses rectangles squares

Describing a Special Parallelogram Decide whether the statement is always, sometimes, or never true. A rhombus is a rectangle. A parallelogram is a rectangle. parallelograms rhombuses rectangles squares

Decide whether the statement is always, sometimes, or never true. A rectangle is a square. A square is a rhombus.

Using Properties of Special Parallelograms ABCD is a rectangle. What else do you know about ABCD?

 QRST is a square. What else do you know about QRST?

Corollaries About Special Quadrilaterals Rectangle Corollary A quadrilateral is a rectangle if and only if it has: Rhombus Corollary A quadrilateral is a rhombus if and only if it has: Square Corollary A quadrilateral is a square if and only if:

Using Properties of a Rhombus PQRS is a rhombus. What is the value of y? 1. Definition of a rhombus 2. Substitute given values 3. Simplify and solve for y P Q 2y + 3 S R 5y – 6

ABCD is a rectangle and mB = 8x + 26. What is the value of x?

Using Diagonals of Special Parallelograms Theorem 6.11 A parallelogram is a rhombus if and only if ABCDis a rhombus iff Theorem 6.12 A parallelogram is a rhombus if and only if: Theorem 6.13 A parallelogram is a rectangle if and only if: ABCDis a rectangle iff

Checking a Rectangle You are building a rectangular frame for a theater set. First, you nail four pieces of wood together. What is the shape of the frame? Using a straight edge, how could you determine if it is a rectangle? 4 ft 6 ft 6 ft 4 ft

Assignment • Page 351 #3-21, 25-43, 56, and 58

Properties of Special Parallelograms