Holt McDougal Geometry 3-1 Lines and Angles Warm Up Identify each of the following. 1. points that lie in the same plane 2.two angles whose sum is 180° 3.the intersection of two distinct intersecting lines 4. a pair of adjacent angles whose non-common sides are opposite rays coplanar points supplementary angles point linear pair

Holt McDougal Geometry 3-1 Lines and Angles Identify parallel, perpendicular, and skew lines. Identify the angles formed by two lines and a transversal. Objectives

Holt McDougal Geometry 3-1 Lines and Angles

Holt McDougal Geometry 3-1 Lines and Angles Example 1: Identifying Types of Lines and Planes Identify each of the following. A. a pair of parallel segments B. a pair of skew segments C. a pair of perpendicular segments D. a pair of parallel planes LM ||QR KN and PQ NS  SP plane NMR || plane KLQ

Holt McDougal Geometry 3-1 Lines and Angles Check It Out! Example 1 Identify each of the following. a. a pair of parallel segments b. a pair of skew segments d. a pair of parallel planes c. a pair of perpendicular segments BF || EJ BF and DE are skew. BF  FJ plane FJH || plane BCD

Holt McDougal Geometry 3-1 Lines and Angles

Holt McDougal Geometry 3-1 Lines and Angles Example 2: Classifying Pairs of Angles Give an example of each angle pair. A. corresponding angles B. alternate interior angles C. alternate exterior angles 1 and 5 D. same-side interior angles 3 and 5 1 and 7 3 and 6

Holt McDougal Geometry 3-1 Lines and Angles Check It Out! Example 2 Give an example of each angle pair. A. corresponding angles B. alternate interior angles C. alternate exterior angles 1 and 3 D. same-side interior angles 2 and 7 1 and 8 2 and 3

Holt McDougal Geometry 3-1 Lines and Angles To determine which line is the transversal for a given angle pair, locate the line that connects the vertices. Helpful Hint

Holt McDougal Geometry 3-1 Lines and Angles Example 3: Identifying Angle Pairs and Transversals Identify the transversal and classify each angle pair. A. 1 and 3 B. 2 and 6 C. 4 and 6 transversal l corr. s transversal n alt. int s transversal m alt. ext s

Holt McDougal Geometry 3-1 Lines and Angles

Holt McDougal Geometry 3-1 Lines and Angles

Holt McDougal Geometry 3-1 Lines and Angles

Holt McDougal Geometry 3-1 Lines and Angles

Holt McDougal Geometry 3-1 Lines and Angles Students will… Use the angles formed by a transversal to prove two lines are parallel. Objective

Holt McDougal Geometry 3-1 Lines and Angles Remember! Converse of a theorem is found by exchanging the hypothesis and conclusion. ***The converse of a theorem is not automatically true. If it is true, it must be stated as a postulate or proved as a separate theorem.

Holt McDougal Geometry 3-1 Lines and Angles

Holt McDougal Geometry 3-1 Lines and Angles

Holt McDougal Geometry 3-1 Lines and Angles Use the given information and the theorems you have learned to show that r || s. 4  8 4  84 and 8 are alternate exterior angles. r || sConv. Of Alt. Ext. s Thm.

Holt McDougal Geometry 3-1 Lines and Angles Use the given information and the postulates you have learned to show that l || m. 1  31 and 3 are corresponding angles. ℓ || m Conv. of Corr. s Post.

Holt McDougal Geometry 3-1 Lines and Angles Which postulate proves that ℓ || m? m3 = (4x – 80)°, m7 = (3x – 50)°, x = 30 m3 = 4(30) – 80 = 40Substitute 30 for x. m7 = 3(30) – 50 = 40Substitute 30 for x. ℓ || m Conv. of Corr. s Post. 3  7 Def. of  s. m3 = m7

Holt McDougal Geometry 3-1 Lines and Angles

Holt McDougal Geometry 3-1 Lines and Angles

Holt McDougal Geometry 3-1 Lines and Angles

Holt McDougal Geometry 3-1 Lines and Angles