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?

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Presentation transcript:

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. Exterior Interior r s Transversal t

Angles formed by Transversals Alternate interior angles interior

Angles formed by Transversals Alternate exterior angles exterior

Angles formed by Transversals Same-side interior angles interior

Angles formed by Transversals Corresponding angles

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 pq r

Five Step Deductive Proof 1.Rewrite the conjecture to be proved in if-then form. 2.Draw and label a figure to represent the given information. 3.State the statement to be proved in terms of the figure. 4.Plan the proof. Find a logical sequence of steps. 5.Demonstrate the argument by putting your plan into writing justifying every statement.

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 B C D E State: Given: Prove:

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.

What are the five steps in a deductive proof? 1.Rewrite the conjecture to be proved in if- then form. 2.Draw and label a figure to represent the given information. 3.State the statement to be proved in terms of the figure. 4.Plan the proof. Find a logical sequence of steps. 5.Demonstrate the argument by putting your plan into writing justifying every statement.

Assignment Page 219, 1-5, 9-10,

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