Questions and Answers
What does the Corresponding Angles Postulate state?
If any two lines are crossed by a transversal and the corresponding angles are congruent, then the lines are parallel.
True
What are Alternate Interior Angles?
The pair of angles that are inside the two lines and on opposite sides of the transversal.
If two parallel lines are crossed by a transversal, then each pair of alternate interior angles is congruent.
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If a pair of alternate interior angles are congruent, then the two coplanar lines crossed by the transversal are parallel.
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What are Same Side Interior Angles?
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If two parallel lines are crossed by a transversal, then each pair of same-side interior angles is supplementary.
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If a pair of same-side interior angles is supplementary, then the two coplanar lines crossed by the transversal are parallel.
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What are Alternate Exterior Angles?
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If two parallel lines are crossed by a transversal, then each pair of alternate exterior angles is congruent.
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If a pair of alternate exterior angles is supplementary, then the two coplanar lines crossed by the transversal are parallel.
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If a transversal is perpendicular to one of two parallel lines, then it is also perpendicular to the other line.
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Study Notes
Corresponding Angles Postulate
- If two parallel lines intersected by a transversal, the corresponding angles formed are always congruent.
Converse of Corresponding Angles Postulate
- If a transversal crosses two lines and the corresponding angles are congruent, then those two lines are parallel.
Alternate Interior Angles
- These angles are located inside the two parallel lines and are positioned on opposite sides of the transversal.
Alternate Interior Angles Theorem
- When two parallel lines are intersected by a transversal, each pair of alternate interior angles created is congruent.
Converse of Alternate Interior Angles Theorem
- If two coplanar lines intersected by a transversal have a congruent pair of alternate interior angles, the lines must be parallel.
Same Side Interior Angles
- These angles are found inside the two parallel lines and on the same side of the transversal.
Same-side Interior Angles Theorem
- For two parallel lines crossed by a transversal, the same-side interior angles are always supplementary (sum to 180 degrees).
Converse of Same Side Interior Angles Theorem
- If a transversal intersects two coplanar lines such that a pair of same-side interior angles are supplementary, then those lines are parallel.
Alternate Exterior Angles
- These angles exist outside the two parallel lines and are positioned on opposite sides of the transversal.
Alternate Exterior Angles Theorem
- When two parallel lines are crossed by a transversal, each pair of alternate exterior angles formed is congruent.
Converse of Alternate Exterior Angles Theorem
- If two coplanar lines are crossed by a transversal and a pair of alternate exterior angles are congruent, then the lines are parallel.
Perpendicular Transversal Theorem
- In a plane, if a transversal is perpendicular to one of two parallel lines, it is also perpendicular to the other line.
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Description
Test your knowledge of the angle theorems in geometry with these flashcards. Each card defines important concepts such as the Corresponding Angles Postulate and Alternate Interior Angles, and helps reinforce your understanding of their implications in geometric proofs.
