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Parallel Lines and Transversals . Angles and parallel lines.

Parallel Lines and Transversals . Angles and parallel lines.  Video. Lesson Objective. Explore relationships of the angles formed by a transversal cutting parallel lines. Vocabulary

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Parallel Lines and Transversals . Angles and parallel lines.

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  1. Parallel Lines and Transversals. Angles and parallel lines.  Video Lesson Objective Explorerelationships of the angles formed by a transversal cutting parallel lines. Vocabulary Parallel lines, parallel planes, transversal, consecutive interior angels, alternative exterior angels, alternative interior angels, corresponding angels.

  2.  Parallel Lines: Coplanar lines that do not intersect. l d c x s w x l

  3. Name all segments that are parallel to Answer: Example 1-1c H E B A F G D C

  4. Answer: Answer: Answer: Example 1-1e Use the figure to name each of the following. Answer: plane XYZ

  5. Transversal: A line that intersects two or more lines in a plane at different points. Transversal crossing two lines This transversal crosses two parallel lines This transversal cut across three lines

  6. Transversal and angles  m k transversal m 1 2 4 3 k 5 6 8 7 1 2 7 8 3 4 5 6 3 6 4 5 1 7 2 8 3 5 4 6 1 5 2 6 3 7 4 8

  7. Corresponding Angles Postulate If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent. m k @ m 5 1 1 2 @ 3 7 3 4 k 6 @ 5 2 6 7 8 @ 4 8

  8. When two parallel lines are cut by a transversal, then…. ….each pair of alternative interior angles is congruent. @ @ 3 6 4 5 ….each pair of alternative exterior angles is congruent.  geogebra @ @ 1 8 2 7 ….each pair of consecutive interior angles is supplementary. 1 2 3 4 m4+ m6=180 6 5 m3+ m5=180 7 8

  9. In the figure and Find Example 2-1a Corresponding Angles Postulate Vertical Angles Theorem Transitive Property Definition of congruent angles Substitution Answer:

  10. In the figure and Find Answer: Example 2-1b

  11. Be sure to identify it correctly on the figure. Use an auxiliary line. Example 2-2a Grid-In Test ItemWhat is the measure of RTV? Read the Test Item

  12. Example 2-2b Solve the Test Item Alternate Interior Angles Theorem Definition of congruent angles Substitution

  13. Example 2-2c Alternate Interior AnglesTheorem Definition of congruent angles Substitution Angle Addition Postulate Write each digit of 125 in a column of the grid. Then shade in the corresponding bubble in each column.

  14. Example 2-2c Answer:

  15. Answer: Example 2-2d Grid-In Test ItemWhat is the measure ofIGE? K J

  16. If and find x and y. by the Corresponding Angles Postulate. Example 2-3e ALGEBRA Find x.

  17. by the Alternate Exterior Angles Theorem. Example 2-3f Definition of congruent angles Substitution Subtract x from each side and add 10 to each side. Find y. Definition of congruent angles Substitution

  18. Example 2-3g Simplify. Add 100 to each side. Divide each side by 4. Answer:

  19. and ALGEBRA If find x and y. Example 2-3h Answer:

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