Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
3-1 Lines and Angles Warm Up Identify each of the following. 1. points that lie in the same plane coplanar points 2. two angles whose sum is 180° supplementary angles 3. the intersection of two distinct intersecting lines point 4. a pair of adjacent angles whose non-common sides are opposite rays linear pair Holt McDougal Geometry 3-1 Lines and Angles Objectives Identify parallel, perpendicular, and skew lines. Identify the angles formed by two lines and a transversal. 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 LM ||QR B. a pair of skew segments KN and PQ C. a pair of perpendicular segments NS SP D. a pair of parallel planes 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 BF || EJ b. a pair of skew segments BF and DE are skew. c. a pair of perpendicular segments BF FJ d. a pair of parallel planes 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 1 and 5 B. alternate interior angles 3 and 5 C. alternate exterior angles 1 and 7 D. same-side interior angles 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 1 and 3 B. alternate interior angles 2 and 7 C. alternate exterior angles 1 and 8 D. same-side interior angles 2 and 3 Holt McDougal Geometry 3-1 Lines and Angles Helpful Hint To determine which line is the transversal for a given angle pair, locate the line that connects the vertices. 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 transversal l corr. s B. 2 and 6 transversal n alt. int s C. 4 and 6 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 Objective Students will… Use the angles formed by a transversal to prove two lines are parallel. 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 84 and 8 are alternate exterior angles. r || s Conv. 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 Holt McDougal Geometry Conv. of Corr. s Post. 3-1 Lines and Angles Which postulate proves that ℓ || m? m3 = (4x – 80)°, m7 = (3x – 50)°, x = 30 m3 = 4(30) – 80 = 40 Substitute 30 for x. m7 = 3(30) – 50 = 40 Substitute 30 for x. m3 = m7 3 7 ℓ || m Holt McDougal Geometry Def. of s. Conv. of Corr. s Post. 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