Parallel Lines Transversal Angles Test – Geometry Math (Printable PDF)

Question 1 Name the pairs (2 points)

Lines a and b are cut by a transversal and the angles are numbered as shown.

1. Name the relationship of ∠4 and ∠5. (1 point)
2. Name the relationship of ∠1 and ∠8. (1 point)

Question 2 Find three angles (3 points)

Lines a and b are parallel and m∠2 = 61°.

1. Find m∠6. (1 point)
2. Find m∠4. (1 point)
3. Find m∠7. (1 point)

Question 3 Alternate interior equation (2 points)

Lines a and b are parallel. Alternate interior angles measure (4x + 11)° and (6x − 19)°. Find x and the measure of each angle.

Question 4 Decide if lines are parallel (3 points)

A transversal crosses two lines. State whether the lines must be parallel and give a reason.

1. Corresponding angles measure 76° and 76°. (1 point)
2. Alternate interior angles measure 64° and 66°. (1 point)
3. Same-side interior angles measure 105° and 75°. (1 point)

Question 5 Parallel with same-side angles (2 points)

Same-side interior angles formed by a transversal measure (7x + 4)° and (5x + 20)°. Find x so that the two lines are parallel, then find both angle measures.

Question 6 Prove lines parallel (3 points)

Given: ∠2 ≅ ∠7. Prove: a ∥ b. Use the numbering in the figure and complete a two-column proof.

Question 7 Equidistant point (3 points)

Point P is on the perpendicular bisector of AB, where AB = 48. PA = (2x + 9) and PB = (4x − 7).

1. Find x. (1 point)
2. Find PA. (1 point)
3. Find the distance from P to the midpoint of AB. (1 point)

Question 8 Crossing bike lanes (2 points)

Two bike lanes run parallel. A crosswalk crosses both. On the first lane, the angle between the crosswalk and the lane is 38° on the east side. Find the matching angle on the second lane and the same-side interior angle that is its neighbor.