## Special Angles on Parallel Lines

On this web page you can investigate the properties of the angles that are formed when a transversal cuts two parallel lines.

### Sketch

A transversal intersecting two lines creates eight different angles: four pairs of corresponding angles, two pairs of alternate interior angles, and two pairs of alternate exterior angles. Use this sketch to study the relationships between the angles in each of these pairs. The sketch below shows parallel lines AB and CD with transversal PQ. Drag points A, P, or Q to change the sketch. Press the buttons to get the measures of the angles. Press Start Over at any time to remove the measurements.

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Investigate

1. When you press Corresponding Angles, you see angles GPA and PQC. What is another pair of corresponding angles?
1. GPA and EQD
2. BPG and DQP
3. BPG and APQ
2. Name another pair of alternate interior angles besides APQ and DQP.
3. Name all pairs of alternate exterior angles.
4. What do you notice about corresponding angles?
5. What do you notice about alternate interior angles?
6. What do you notice about alternate exterior angles?
7. Formulate the Parallel Lines Conjecture: If two parallel lines are cut by a transversal, then corresponding angles are _____, alternate interior angles are _____, and alternate exterior angles are _____.

### Sketch

What happens if the lines you start with are not parallel? In the sketch here, transversal PQ cuts lines AB and CD. Drag points A, C, P, or Q to change the sketch. Observe what happens to the angle measures when the lines are not parallel.

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Investigate

1. Is your conjecture still true when the lines are not parallel?
2. Use this sketch to investigate the Converse of the Parallel Lines Conjecture: If two lines are cut by a transversal to form pairs of congruent corresponding angles, congruent alternate interior angles, or congruent alternate exterior angles, then the lines are _____.