Download 3.2 Use Parallel Lines and Transversals

Geometry Chapter 3: Parallel and Perpendicular Lines 3.2-­‐ Use Parallel Lines and Transversals SWBAT: use angles formed by parallel lines and transversals. Common Core: G.CO.9
“Do Now”
Classify each pair as corresponding, alternate interior, alternate exterior, or consecutive interior
angles.
Postulate 15: Corresponding Angle Postulate If two lines are cut by a transversal, then the pairs of corresponding angles are _____________________. Theorem 3.1: Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then the pairs of __________________________________ angles are congruent. Geometry Chapter 3: Parallel and Perpendicular Lines Theorem 3.2: Alternate Exterior Angles Theorem If two parallel lines are cut by a _______________________________, then the pairs of alternate exterior angles are congruent. Theorem 3.3: Consecutive Interior Angles Theorem If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are _________________________________. Example 1: The measure of three of the numbered angles is 120°. Identify the angles and explain why they measure 120°. Example: The measure of three of the numbered angles is 55°. Identify the angles and explain why they measure 55°. Geometry Chapter 3: Parallel and Perpendicular Lines Example 2: Find the value of x. Example: Find the value of x. Practice: Use the diagram at the right. 1. If 𝑚∠1 = 105°, find 𝑚∠4, 𝑚∠5, 𝑎𝑛𝑑 𝑚∠8. Tell which postulate or theorem you use in each case. 2. If 𝑚∠3 = 68° and 𝑚∠8 = (2𝑥 + 4)°, what is the value of x? Show your steps. Geometry Chapter 3: Parallel and Perpendicular Lines Example 3: Prove that if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. Given: 𝒑 ∥ 𝒒 Prove: ∠1 ≅ ∠2 Statements Reasons Example: Prove that if two parallel lines are cut by a transversal, then the exterior angles on the same side of the transversal are supplementary. Given: 𝒑 ∥ 𝒒 Prove: ∠1 𝑎𝑛𝑑 ∠2 are supplementary Statements Reasons Geometry Chapter 3: Parallel and Perpendicular Lines Example 4: The figure shows a balance scale. If 𝑚∠1 = 70°, what is 𝑚∠2? How do you know? Example: Homework: Pgs. 157 – 158 #’s 3 – 35 ODD