CHAPTER 6 LESSON 2Properties of Parallelograms

Warm-up

ASAHGE GHEHEG GH

HE EG

They are parallel.

Theorem 6.1 Opposite sides of a parallelogram are

congruent.

Consecutive Angles Angles of a polygon that share a side are

consecutive angles. Because opposite sides of a parallelogram

are parallel, consecutive angles are same-side interior angles

They are therefore SUPPLEMENTARY. ∠a and ∠d are consecutive angles m∠a + m∠d = 180

Theorem 6-2 Opposite angles of a parallelogram are

congruent Opposite angles are supplementsof the same angle.

Therefore, they are congruent.

Theorem 6-3 The diagonals of a parallelogram bisect

each other

Proof of Theorem 6.3 Given: Parallelogram ABCD Prove: AC and BD bisect each other at

point O If ABCD is a parallelogram, thenAB and DC are parallel. ∠1 4 and 2 3 because ≅ ∠ ∠ ≅ ∠alternate Interior angles are congruent. AB ≅ DC because opposite sidesof a parallelogram are congruent. ∆ADO ≅ ∆BCO by ASA AE≅CE and BE≅DE by CPCTC

1

2

3

4

Theorem 6.4 If three or more parallel lines cut off

congruent segments on one transversal, then they cut off congruent segments on every transversal.

Example 1: Using Consecutive Angles

What is the measure of ∠P?

Consecutive angles are supplementary

64 + P = 180 P = 180 – 64 P = 116

Your Turn!

Consecutive angles are supplementary

86 + P = 180 P = 180 –86P = 94

Example 2: Proofs

Proof #2

Example 3: Algebra

Your Turn! Algebra

Example 4: Parallel Lines and Transversals

Lesson Quiz