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Transversals and Angles 3-4A

Transversals and Angles 3-4A. What is a transversal? What are four types of angles made by a transversal? What are the five steps in a deductive proof?. Definition. A transversal is a line that intersects two coplanar lines at two different points. Transversal t. Exterior. 1. 2. 4. 3.

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Transversals and Angles 3-4A

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  1. Transversals and Angles 3-4A What is a transversal? What are four types of angles made by a transversal? What are the five steps in a deductive proof?

  2. Definition A transversal is a line that intersects two coplanar lines at two different points. Transversal t Exterior 1 2 4 3 r Interior 5 6 s 8 7 Exterior

  3. interior Angles formed by Transversals Alternateinteriorangles 1 2 4 3 5 6 8 7

  4. exterior 4 3 5 6 exterior Angles formed by Transversals Alternateexteriorangles 1 2 8 7

  5. Angles formed by Transversals Same-sideinteriorangles 1 2 4 interior 3 5 6 8 7

  6. Angles formed by Transversals Correspondingangles 1 2 4 3 5 6 8 7

  7. p q 1 2 3 4 8 7 6 5 r Try It Name: The transversal Two pairs of same side interior Two pairs of alternate exterior angles Two pairs of alternate interior angles Four pairs of corresponding angles

  8. Five Step Deductive Proof • Rewrite the conjecture to be proved in if-then form. • Draw and label a figure to represent the given information. • State the statement to be proved in terms of the figure. • Plan the proof. Find a logical sequence of steps. • Demonstrate the argument by putting your plan into writing justifying every statement.

  9. Do the rewrite, draw, and state steps All vertical angles are congruent. Rewrite: If two angles are vertical angles, then they are congruent. Draw: two angles are vertical angles A C D E B State: Given: Prove:

  10. What is a transversal? A transversal is a line that intersects two coplanar lines at two different points. • What are four types of angles made by a transversal? Alternate interior angles, alternate exterior angles, same-side interior angles and corresponding angles.

  11. What are the five steps in a deductive proof? • Rewrite the conjecture to be proved in if-then form. • Draw and label a figure to represent the given information. • State the statement to be proved in terms of the figure. • Plan the proof. Find a logical sequence of steps. • Demonstrate the argument by putting your plan into writing justifying every statement.

  12. Assignment Page 219, 1-5, 9-10, 19-23.

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