Geometry Parallel Lines and Transversals Worksheet (PDF)

Geometry math worksheet: Parallel Lines and Transversals – Maths PDF

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

These 20 problems practice vertical angles, angle pairs with parallel lines and perpendicular bisectors (Common Core G-CO.C.9). The first problems are quick one-step checks of the definitions and formulas from the lesson. The middle problems ask for diagrams, equations and careful reasoning in the style of a high school Geometry class. The last six problems are applied problems with streets, railings, shelves and equations of bisectors.

Geometry · Common Core State Standards: G-CO.C.9

Parallel lines worksheet: exercises 1 to 10

Exercise 1 – Vertical angles

Two lines intersect. One angle measures \(68^{\circ}\). Find the measure of its vertical angle.

Exercise 2 – Linear pair

Two angles form a linear pair. One measures \(112^{\circ}\). Find the other.

Exercise 3 – Corresponding angles

Parallel lines cut by a transversal.

The two horizontal lines are parallel. Angle 2 measures 65°. Find the measure of angle 6.

Exercise 4 – Alternate interior angles

Parallel lines cut by a transversal.

The horizontal lines are parallel and angle 4 measures 125°. Find the measure of angle 5.

Exercise 5 – Same-side interior angles

Parallel lines are cut by a transversal. Two same-side interior angles are angle 4, measuring \(125^{\circ}\), and angle 6. Find the measure of angle 6.

Exercise 6 – Name the pair

Name the angle-pair relationship for each pair in the figure: 3 and 6, 2 and 6, 4 and 6, 1 and 8.

Exercise 7 – Alternate exterior angles

Parallel lines are cut by a transversal. Angle 1 measures \(118^{\circ}\). Find the measure of angle 8.

Exercise 8 – Corresponding angles with x

Parallel lines cut by a transversal.

Find x and the measure of each angle.

Exercise 9 – Alternate interior with x

Parallel lines are cut by a transversal. Alternate interior angles measure \((4x – 7)^{\circ}\) and \((2x + 25)^{\circ}\). Find \(x\) and the angle measure.

Exercise 10 – Same-side interior with x

Same-side interior angles of parallel lines measure \((6x + 10)^{\circ}\) and \((4x + 20)^{\circ}\). Find \(x\) and both angles.

Exercises 11 and up

Exercise 11 – Vertical angles with x

Two vertical angles measure \((7x – 12)^{\circ}\) and \((4x + 21)^{\circ}\). Find \(x\) and the measure of each.

Exercise 12 – Are the lines parallel? (no)

A transversal crosses two lines. A pair of corresponding angles measures \(74^{\circ}\) and \(76^{\circ}\). Are the lines parallel? Explain.

Exercise 13 – Are the lines parallel? (yes)

Alternate interior angles.

A transversal makes alternate interior angles of 112° and 112°. Are the lines parallel? Explain.

Exercise 14 – All eight angles

Parallel lines are cut by a transversal. One angle measures \(57^{\circ}\). Find the measures of all eight angles.

Exercise 15 – Perpendicular bisector

Every point on the perpendicular bisector of AB is equally far from A and from B.

Line PM is the perpendicular bisector of segment AB. \(PA = 2x + 5\) and \(PB = 4x – 11\). Find \(x\) and \(PA\).

Exercise 16 – Perpendicular bisector equation

Segment AB and its perpendicular bisector.

Find an equation of the perpendicular bisector of the segment with endpoints A(-2, 1) and B(6, 5).

Exercise 17 – Crossing streets

Two parallel streets, Maple and Oak, are cut by a diagonal avenue. At Maple Street the acute angle on the north-east side is 52°. Find the angle on the same side at Oak Street if it is the corresponding angle, and find the obtuse angle next to it.

Exercise 18 – Railing

The two parallel rails of a staircase are crossed by a post. The post makes an angle of 64° with the upper rail. What angle does it make with the lower rail on the same side (same-side interior), if the 64° angle is also inside the rails?

Exercise 19 – Shelf bracket

A shelf is parallel to the floor. A bracket meets the shelf at \((3x + 12)^{\circ}\) and meets a parallel rail at \((5x – 8)^{\circ}\) as alternate interior angles. Find x and the angle.

Exercise 20 – Equal distance

Towns A and B are 10 miles apart. Priya’s house P lies on the perpendicular bisector of the road between them and is 13 miles from A. How far is P from B, and how far is P from the midpoint M of AB?

Key facts behind this parallel lines worksheet

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 worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the parallel lines worksheet as a PDF with the button below and keep it with your notes.

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