Geometry Parallel Lines and Transversals Test with Point Values (PDF)

Geometry math test: Parallel Lines and Transversals – Maths PDF

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This parallel lines test for Geometry covers parallel lines and transversals (Common Core G-CO.C.9), with a free PDF to print.

This 45-minute test checks angles formed by a transversal, vertical angles and perpendicular bisectors. It has 9 questions worth 20 points in total. Show every step of the work, label diagrams, and include units where they apply. Calculators are allowed unless the teacher says otherwise.

Time and points

About this test

Grade: Geometry
Chapter: Parallel Lines and Transversals
Standards: G-CO.C.9
Time: 45 minutes
Total: 20 points

Parallel lines test: questions

Question 1 – Name the pairs [2 pts]

Parallel lines cut by a transversal.

Name the relationship of angles 3 and 5. (1 point)
Name the relationship of angles 1 and 8. (1 point)

Question 2 – Solve for x [3 pts]

Parallel lines.

Find x. (1 point)
Find the measure of each angle. (1 point)
Find the measure of the angle that forms a linear pair with angle (5x – 3). (1 point)

Question 3 – Vertical and linear [2 pts]

Two lines intersect. One angle is \((2x + 20)^{\circ}\) and its adjacent angle is \((3x – 10)^{\circ}\). Find x and all four angle measures.

Question 4 – Prove parallel [2 pts]

Two lines and a transversal.

A transversal crosses two lines, and a pair of corresponding angles measures 80° and 82°. Are the lines parallel? Explain.

Question 5 – Same-side interior [2 pts]

Parallel lines are cut by a transversal. Same-side interior angles measure (7x + 3)° and (5x + 9)°. Find x and both angle measures.

Question 6 – Perpendicular bisector [3 pts]

Line PM is the perpendicular bisector of AB.

PA = 3x + 4 and PB = 5x – 8. Find x and PA. (2 points)
AB = 24. Find the length PM if PA = 20. (1 point)

Question 7 – Midpoint and slope [2 pts]

Find the equation of the perpendicular bisector of the segment with endpoints (0, 2) and (8, 6).

Question 8 – Road angles [2 pts]

A bike path crosses two parallel roads. It makes a 73° angle with the first road. Find the measure of the alternate interior angle on the second road and of the same-side interior angle.

Question 9 – Explain [2 pts]

Explain why vertical angles are congruent, using the fact that a linear pair adds to 180°.

Key facts behind this parallel lines test

Key facts

Vertical angles are congruent, and a linear pair adds to 180 degrees.
Parallel lines: corresponding and alternate interior angles are congruent.
Parallel lines: same-side interior angles are supplementary.
If those angle conditions hold for a transversal, the two lines are parallel.
Points on the perpendicular bisector of a segment are equidistant from its endpoints.

How to use this parallel lines test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Geometry chapters: Geometry math.

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