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Geometry Warm Up: Lines, Planes, and Angles

This warm up exercise focuses on identifying points, lines, and planes in the same plane, determining angle pairs, and classifying lines as parallel, perpendicular, or skew.

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Geometry Warm Up: Lines, Planes, and Angles

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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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