Problem 1 Classifying Special Parallelograms

Is ▱ A B C D white parallelogram eh b c d a rhombus, a rectangle, or a square? Explain.

▱ A B C D white parallelogram eh b c d is a rectangle. Opposite angles of a parallelogram are congruent so m ∠ D m angle d is 90. By the Same-Side Interior Angles Theorem, m ∠ A = 90 m angle , eh equals 90 and m ∠ C = 90 . m angle . c equals 90 . Since ▱ A B C D white parallelogram eh b c d has four right angles, it is a rectangle. You cannot conclude that ABCD is a square because you do not know its side lengths.

✓ Got It?

1. Is ▱ E F G H white parallelogram e f g h a rhombus, a rectangle, or a square? Explain.

Take note Theorem 6-13

Theorem

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

If…

ABCD is a rhombus

Then …

A C ¯ ⊥ B D ¯ eh c bar , up tack , b d bar

Theorem 6-14

Theorem

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

If…

ABCD is a rhombus

Then …

∠ 1 ≅ ∠ 2 angle , 1 approximately equal to , angle 2

∠ 3 ≅ ∠ 4 angle , 3 approximately equal to , angle 4

∠ 5 ≅ ∠ 6 angle , 5 approximately equal to , angle 6

∠ 7 ≅ ∠ 8 angle , 7 approximately equal to , angle 8

You will prove Theorem 6-14 in Exercise 45.