Parallel Lines Cut by a Transversal Worksheets

Free Parallel Lines Cut by a Transversal Worksheets with Answer Keys

If you’re looking for a free Parallel Lines Cut by a Transversal Worksheet or two to give yourself or your students some extra practice with this important math skill, then you’re in the right place!

This page shares a collection of free PDF Parallel Lines Cut by Transversals Practice Worksheets that you can download and/or print to give yourself plenty of practice opportunities to solve math problems involving parallel lines cut by transversals. Each parallel lines cut by transversal worksheet available in the free library below is available as a printable PDF file that includes an answer key on the second page.

To download any of our free parallel lines cut by a transversal worksheets, simply double-click on any of the blue text links below to open the PDF preview page. From there, you can preview the complete worksheet and the answer key as well. At this point, you will have the option to download and save the worksheet as a PDF file or to send it to your printer to be printed in either color or black-and-white.

This page also includes a review section (directly below the worksheet library) that includes a quick recap of some of the key features and relationships associated with parallel lines cut by transversals. If you are struggling to solve problems on any parallel lines cut by a transversal worksheet, we recommend that you visit this review section to strengthen your understanding before moving forward.

Finally, all of the free PDF worksheets shares below are sample worksheets from the Mashup Math K-12 Infinite Math Worksheet Library available on our website, where we share hundreds and grade and topic-specific practice worksheets with answer keys.

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Parallel Lines Cut by Transversals Worksheets

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Review: Parallel Lines Cut by a Transversal

If you are having trouble with solving problems on any free parallel lines cut by a transversal worksheet above, then this short topic review will surely help you.

One of the most important things for students to understand about parallel lines cut by a transversal are the angle relationships. Every time you have two parallel lines cut by a transversal, there are 8 total angles that are formed, and these angles have consistent relationships. Namely, angles will either be equal to other angles or they will be supplemental to them (i.e. there sum will be equal to 180 degrees).

The more experience that you gain with parallel lines and transversals, the easier it will be to identify these relationships and apply them whenever you are solving problems.

Take a look at the diagram of two parallel lines being cut by a transversal in Figure 01 below.

Notice that there are 8 total angles: ∠a, ∠b, ∠c, ∠a, ∠e, ∠f, ∠g, and ∠h.

Also notice the angles are either acute (less than 90 degrees) or obtuse (greater than 90 degrees).

All of the acute angles will equal the same measure and all of the obtuse angles will equal the same measure:

• Acute Angles: ∠a, ∠d, ∠e, ∠h

• Obtuse Angles: ∠b, ∠c, ∠f, ∠g

With this fact in mind, we can make conclusions such as:

• ∠a=∠d

• ∠b=∠g

• ∠c=∠f

Additionally, since relationship between any acute angle and any obtuse angle formed by parallel lines cut by a transversal is supplementary, we can say that the sum of any acute angle and any obtuse angle will be equal to 180 degrees. For example:

• ∠a + ∠b = 180

• ∠f + ∠h = 180

• ∠c + ∠e = 180

Note that these relationships will always apply whenever you have two or more parallel lines cut by a transversal. In fact, even if the transversal is perpendicular, the relationships will stay the same (although there will be no acute or obtuse angles since every angle will measure 90 degrees.)

For example, take a look at the diagram in Figure 02 below, which features a pair of parallel lines cut by a transversal with the angle measures labeled.

Here we are putting the previously-mentioned angle relationships into practice. Notice that all of the acute angles have a measure of 55 degrees and all of the obtuse angles have a measure of 125 degrees.

And, since 55 + 125 = 180, we can confirm that the relationship between any acute angle and any obtuse angle in the diagram is supplementary.

In fact, as long as you know the measure of any one angle in the entire diagram, you can determine the measures of all of the angles!

For example, if you only knew that the measure of the acute angle was 55 degrees, you could simply solve 180 - 55 = ? to find the measure of the obtuse angles. Since, 180 - 55 = 125, you could conclude that the measure of all of the obtuse angles is 125 degrees.

Do you need a more in-depth review of Parallel Lines Cut by a Transversal?

If so, check out our free step-by-step video tutorial on YouTube and then come back to this page and test your understanding by working on a few of our free parallel lines cut by a transversal worksheets. The more that you study the previously-mentioned angle relationships and practice solving problems, the more skilled you will become!