3.2 – Use Parallel Lines and Transversals

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3.2 – Use Parallel Lines and Transversals. Postulate 15 – Corresponding Angles Postulate If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. . 3.2 – Use Parallel Lines and Transversals. Example 1: Identify congruent angles

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### 3.2 – Use Parallel Lines and Transversals

Postulate 15 – Corresponding Angles Postulate

If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

### 3.2 – Use Parallel Lines and Transversals

Example 1: Identify congruent angles

The measure of three of the numbered angles is 55 degrees. Identify the angles. Explain your reasoning.

What are the measures of the

other angles in the picture?

### 3.2 – Use Parallel Lines and Transversals

Theorem 3.1 – Alternate Interior Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

### 3.2 – Use Parallel Lines and Transversals

Theorem 3.1 – Alternate Exterior Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.

### 3.2 – Use Parallel Lines and Transversals

Theorem 3.1 – Consecutive Interior Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.

### 3.2 – Use Parallel Lines and Transversals

Example 2 – Use properties of parallel lines

Find the value of x.

### 3.2 – Use Parallel Lines and Transversals

Example 3 – Use properties of parallel lines

Find the value of x.

### 3.2 – Use Parallel Lines and Transversals

Example 4 – Use properties of parallel lines

Find the value of x.

### 3.2 – Use Parallel Lines and Transversals

Example 5 – Use properties of parallel lines

Find the value of x and y.

### 3.2 – Use Parallel Lines and Transversals

Example 6 – Use properties of parallel lines

Find the value of x and y.

### 3.2 – Use Parallel Lines and Transversals

Example 7 – Use properties of parallel lines

Find the value of x and y.

### 3.2 – Use Parallel Lines and Transversals

Example 8 – Prove the Alternate Interior Angles Theorem

Prove that if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

### 3.2 – Use Parallel Lines and Transversals

Example 9 – Solve a real world problem.

When sunlight enters a drop of rain, different colors of light leave the drop at different angles. This process is what makes a rainbow. For violet light, m<2 = 40 degrees. What is m<1? How do you know?