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Warm Up Identify each of the following. 1. points that lie in the same plane

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.

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Warm Up Identify each of the following. 1. points that lie in the same plane

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  1. 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

  2. Objectives Identify parallel, perpendicular, and skew lines. Identify the angles formed by two lines and a transversal.

  3. LM ||QR KNand PQ NS SP 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 plane NMR|| plane KLQ

  4. BF || EJ BFand DE are skew. BF FJ Check It Out! Example 1 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 plane FJH || plane BCD

  5. 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

  6. 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

  7. Helpful Hint To determine which line is the transversal for a given angle pair, locate the line that connects the vertices.

  8. 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

  9. Objective Students will… Use the angles formed by a transversal to prove two lines are parallel.

  10. 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.

  11. 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.

  12. Use the given information and the postulates you have learned to show that l || m. 1 3 1 and 3 are corresponding angles. ℓ || mConv. of Corr. s Post.

  13. 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 = 40 Substitute 30 for x. m3 = m7 3  7 Def. of  s. ℓ || m Conv. of Corr. s Post.

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