3-2: Angles Formed by Parallel Lines and Transversals Do NOW 1/15/2019 5:31 PM 3-2: Angles Formed by Parallel Lines and Transversals

Page 148 (Answers may vary) 14) 𝐴𝐵 ∥ 𝐷𝐸 15) 𝐴𝐵 & 𝐶𝐹 are skewed 16) 𝐵𝐷 ⊥ 𝐷𝐹 17) Plane ABC || Plane DEF 18) ∠2 & ∠6 19) ∠1 & ∠8 20) ∠1 & ∠6 21) ∠2 & ∠5 22) Transversal: p; Correspond. 23) Transversal: q; Alt. Int. Ang. 24) Transversal: l; Alt. Ext. Ang. 25) Transversal: p; Same-Side Int. 1/15/2019 5:31 PM 3-2: Angles Formed by Parallel Lines and Transversals

3-2: Angles Formed by Parallel Lines and Transversals 1/15/2019 5:31 PM 3-2: Angles Formed by Parallel Lines and Transversals

Angles Formed by Parallel Lines and Transversals Section 3–2 Geometry PreAP, Revised ©2013 viet.dang@humble.k12.tx.us 1/15/2019 5:31 PM 3-2: Angles Formed by Parallel Lines and Transversals

3-2: Angles Formed by Parallel Lines and Transversals Postulate and Theorem Postulate/Axiom: Describes a fundamental relationship between the basic terms of geometry: Accepted to be true without proof Theorem: A statement or conjecture that can be proven true by undefined terms, definitions and postulates. 1/15/2019 5:31 PM 3-2: Angles Formed by Parallel Lines and Transversals

Postulates Type of Theorem/Postulate Definition Visual Example A) Corresponding Angles Postulate If two parallel lines are cut by a transversal, then pairs of corresponding angles are congruent. B) Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then pairs of alternate interior angles are congruent. C) Alternate Exterior Angle Theorem If two parallel lines are cut by a transversal, then pairs of alternate exterior angles are congruent. D) Consecutive Interior Angles Theorem If two parallel lines are cut by a transversal, then pairs of consecutive interior angles are supplementary. 1/15/2019 5:31 PM 3-2: Angles Formed by Parallel Lines and Transversals

3-2: Angles Formed by Parallel Lines and Transversals Example 1 On the map below, 1st and 2nd Ave. are parallel. A city planner on the triangular island is formed by the intersections of the four streets below. What are the measures of the angles of the garden and park? 1/15/2019 5:31 PM 3-2: Angles Formed by Parallel Lines and Transversals

3-2: Angles Formed by Parallel Lines and Transversals Example 2 Using the diagram below, solve for 𝑚∠𝐸𝐶𝐹 and 𝑚∠𝐷𝐶𝐸 1/15/2019 5:31 PM 3-2: Angles Formed by Parallel Lines and Transversals

3-2: Angles Formed by Parallel Lines and Transversals Example 3 Using the diagram below, solve for 𝑚∠𝐸𝐷𝐺 and 𝑚∠𝐵𝐷𝐺 1/15/2019 5:31 PM 3-2: Angles Formed by Parallel Lines and Transversals

3-2: Angles Formed by Parallel Lines and Transversals Example 4 Using the diagram below, solve for 𝑚∠𝐸𝐷𝐺 and 𝑚∠𝐵𝐷𝐺 1/15/2019 5:31 PM 3-2: Angles Formed by Parallel Lines and Transversals

3-2: Angles Formed by Parallel Lines and Transversals Your Turn Using the diagram below, if 𝑚∠5=2𝑥−10, 𝑚∠6=4 𝑦−25 and 𝑚∠7=𝑥+15, solve for x and y. 1/15/2019 5:31 PM 3-2: Angles Formed by Parallel Lines and Transversals

3-2: Angles Formed by Parallel Lines and Transversals Example 5 What is the measure of 𝑚∠𝐺𝐻𝐼. 1/15/2019 5:31 PM 3-2: Angles Formed by Parallel Lines and Transversals

3-2: Angles Formed by Parallel Lines and Transversals Your Turn What is the measure of 𝑚∠𝐺𝐻𝐼. 1/15/2019 5:31 PM 3-2: Angles Formed by Parallel Lines and Transversals

3-2: Angles Formed by Parallel Lines and Transversals Assignment Page 158 7-27 odd (omit 25), 28, 31, 37 1/15/2019 5:31 PM 3-2: Angles Formed by Parallel Lines and Transversals