Parallel Lines & Transversals Flashcards

Parallel lines l and m are cut by a transversal. One alternate interior angle measures 65°. What does the other alternate interior angle measure?

Answer: 65°

Alternate interior angles are congruent when lines are parallel, so both measure 65°.

Which angle relationship, when congruent, proves that two lines cut by a transversal are parallel?

Answer: Corresponding angles

If corresponding angles are equal, the lines are parallel by the Converse of the Corresponding Angles Postulate.

When a transversal crosses two parallel lines (not at 90°), how many distinct angle measures are formed among the 8 angles?

Answer: 2

Due to parallel line properties, all 8 angles take only 2 distinct values — one angle and its supplement.

Consecutive interior angles formed by two parallel lines and a transversal are also known as _____.

Answer: co-interior angles

Consecutive interior angles (same-side interior angles) are also called co-interior angles.

Two parallel lines are cut by a transversal forming co-interior angles of 3x° and (2x + 10)°. What is x?

Answer: 34

Co-interior angles sum to 180°: 3x + 2x + 10 = 180, so 5x = 170 and x = 34.

Line l is parallel to line m. A transversal creates an angle of 72° with line l. What is the corresponding angle with line m?

Answer: 72°

Corresponding angles are congruent when lines are parallel, so the angle with line m is also 72°.

Two parallel lines are cut by a transversal. One of the eight angles measures 40°. How many of the eight angles measure 140°?

Answer: 4

The 8 angles consist of two distinct measures: 40° and its supplement 140°. Exactly four angles measure each value.