6-4 Properties of Rhombuses, Rectangles, and Squares

Special Parallelograms

Problem 1: Classifying Parallelograms

Theorem 6-13

If a parallelogram is a rhombus, then its diagonals are perpendicular

Theorem 6-14

If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles

Problem 2: Finding Angle Measures

What are the measures of the numbered angles in rhombus ABCD?

What are the measures of the numbered angles in rhombus PQRS?

Theorem 6-15

If a parallelogram is a rectangle, then its diagonals are congruent

Problem 3: Finding Diagonal Length

In rectangle RSBF, 𝑆𝐹 = 2𝑥 + 15 and 𝑅𝐵 = 5𝑥 − 12 . What is the length of a diagonal?