Two parallel lines are cut by a transversal. Which statements are true for all such cases? Select three that apply. A Each pair of vertical angles is congruent.

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
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**Question:**

Two parallel lines are cut by a transversal. Which statements are true for all such cases? Select *three* that apply.

A. ☐ Each pair of vertical angles is congruent.

B. ☐ Each pair of corresponding angles is congruent.

C. ☐ Each pair of supplementary angles is congruent.

D. ☐ Each pair of alternate interior angles is congruent. 

**Explanation:**

- When two parallel lines are intersected by a transversal, certain pairs of angles are congruent or supplementary. 
- **Vertical Angles**: Opposite angles formed by two intersecting lines are always congruent.
- **Corresponding Angles**: Angles in the same relative position at each intersection where a transversal crosses parallel lines are congruent.
- **Supplementary Angles**: Consecutive interior angles on the same side of the transversal are not congruent but are supplementary (they add up to 180 degrees).
- **Alternate Interior Angles**: Angles that lie between the two lines on opposite sides of the transversal are congruent.
Transcribed Image Text:**Question:** Two parallel lines are cut by a transversal. Which statements are true for all such cases? Select *three* that apply. A. ☐ Each pair of vertical angles is congruent. B. ☐ Each pair of corresponding angles is congruent. C. ☐ Each pair of supplementary angles is congruent. D. ☐ Each pair of alternate interior angles is congruent. **Explanation:** - When two parallel lines are intersected by a transversal, certain pairs of angles are congruent or supplementary. - **Vertical Angles**: Opposite angles formed by two intersecting lines are always congruent. - **Corresponding Angles**: Angles in the same relative position at each intersection where a transversal crosses parallel lines are congruent. - **Supplementary Angles**: Consecutive interior angles on the same side of the transversal are not congruent but are supplementary (they add up to 180 degrees). - **Alternate Interior Angles**: Angles that lie between the two lines on opposite sides of the transversal are congruent.
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