3.2 BUILDING ON 3.1… Relationships for angle pairs of parallel lines with a transversal: corresponding angles alternate interior angles alternate exterior angles same-side interior angles (consecutive interior) same-side exterior angles (consecutive exterior)

Theorem 3.1: Corresponding Angles Theorem NOTE: Many textbooks state this as a postulate however this author argues that a parallel line is a rigid transformation and thus the angles are also a rigid transformation.

Example 1: Using the Corresponding Angles Postulate Find each angle measure. A. mECF B. mDCE

Check It Out! Example 1 Find mQRS.

Proofs for these theorems? 3-2 3-3 3-4 Proofs for these theorems?

Example 2: Finding Angle Measures Find each angle measure. A. mEDG B. mBDG

Check It Out! Example 2 Find mABD.

Example 3: Music Application Find x and y in the diagram.

Lesson Quiz State the theorem that is related to the measures of the angles in each pair. Then find the unknown angle measures. 1. m1 = 120°, m2 = (60x)° 2. m2 = (75x – 30)°, m3 = (30x + 60)° 3. m3 = (50x + 20)°, m4= (100x – 80)° 4. m3 = (45x + 30)°, m5 = (25x + 10)°