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?

DefinitionA transversal is a line that intersects two

coplanar lines at two different points.

Exterior

Exterior

Interior

12

34

5 6

78

r

s

Transversal t

Angles formed by Transversals

Alternate interior angles

6&4 5&3

1 2

34

5 6

78

interior

Angles formed by Transversals

Alternate exterior angles

7&1

1 2

34

5 6

78

8&2

exterior

exterior

Angles formed by Transversals

Same-side interior angles

5&4

1 2

34

5 6

78

6&3

interior

Angles formed by Transversals

Corresponding angles

5&1

1 2

34

5 6

78

6&2 7&3 8&4

Try ItName:

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

1 2 3 45678

p q

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 stepsAll vertical angles are congruent.

Rewrite: If two angles are vertical angles, then they are congruent.

Draw: two angles are vertical angles

angles.verticalareand CBDABE

A

B

C

DE

State: Given:

Prove: CBDABE

• 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, 19-23.