4 Useful Tips about Parallel Lines Cut by a Transversal

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A Short Explanation of Parallel Lines and Transversals

Parallel Lines cut by a Transversal are formed when two parallel lines are intersected diagonally by an additional line. This additional line is called a transversal. When two Angles in Parallel Lines happen, there are four types of congruent angles that are formed and can be used to solve for missing angles. The first type of congruent angle formed by Angles in Parallel Lines are Vertical Angles. Vertical Angles are angles that are located diagonally across from each other. The second type of congruent angles are Corresponding Angles. Corresponding angles are located in the same location but on each different parallel line. The third type of congruent angles are Alternate Exterior Angles, which are angles that are on the exterior of the figure and also on the opposite side of the transversal. The last type of congruent angle formed by Parallel Lines and Transversals are Alternate Interior Angles, which are angles that are on the interior of the figure and also on the opposite side of the transversal.

Common Core Standard: 8.G.5

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Here’s how to solve Parallel Lines cut by a Transversal Example Problems

Parallel Lines and Transversals are formed when two parallel lines are crossed by an extra line. This extra line is known as transversal lines. These two things make up all two parallel lines cut by a transversal problems. At the point when two Angles in Parallel Lines occur, there are four kinds of points that are formed and can be used to solve for missing angles. The main kind of angles are Vertical Angles. Vertical Angles will be points that are found corner to corner opposite one another. The second sort of angles are Corresponding Angles. Relating angles are situated in a similar area yet on each unique parallel line. The third kind of compatible points are Alternate Exterior Angles, which are edges that are on the outside of the figure and furthermore on the contrary side of the transversal. The last sort of angle formed by Parallel Lines are Alternate Interior Angles, which are edges that are on the inside of the figure and furthermore on the contrary side of the transversal.

4 Steps for finding the Angles in Parallel Lines and Transversals

Parallel Lines are two lines that will never cross.
A transversal is a line that intersect the parallel lines.
Vertical angles are diagonally across from each other and are congruent.
Corresponding angle occur in the spot for both intersection points of the transversal and parallel lines.

Parallel Lines Cut by a Transversal Practice Problems Quiz

Watch the video explanation of our Parallel Lines cut by a Transversal Worksheet

Watch our free video on how to solve Angles in Parallel Lines. This video shows how to solve problems that are on our free Parallel Lines and Transversals worksheet that you can get by submitting your email above.

Watch the free Parallel Lines and Transversals video on YouTube here: Parallel Lines cut by a Transversal

Video Transcript:

This video is about parallel lines and transversals. We’re going to go through some problems that you can find on our two parallel lines cut by a transversal worksheet on our website.

Let’s jump down to number one about two parallel lines are crossed by a transversal. This is the first problem on the free parallel lines and transversal worksheet that you can download above. The first thing we need to go over are the parts of the parallel lines cut by transversal. These two lines here are parallel lines and parallel lines are lines that will never cross. Think of them as railroad tracks or the outside parts of a ladder so they’ll never cross. Then the line that does cross them is called the transversal which is this part right here. When we talk about or when I say parallel lines we’re talking about these lines here and then the line that goes across the parallel lines is the transversal.

Now when you’re solving for angles that are missing in parallel lines cut by transversal there are a few key things that you need to remember. The easiest two things to remember are vertical angles and corresponding angles. Now vertical angles are any angles that are diagonal across the parallel line and the transversal in the case of this problem 60 and X are vertical angles. 60 and X and vertical angles and all vertical angles are congruent. I automatically know that if this is 60 and because this is the diagonal across from it, it also has to be 60. If we knew this angle here let’s just call it question mark then the angle across from it here would also be question mark it would be exactly the same moving on the find Y uses.

The second most important thing to remember when doing parallel lines & transversals worksheet and that’s called corresponding angles. Now a corresponding angle is located in the same position at each of the intersections of the transversal. If you’re looking you notice that the transversal creates four angle each time across as a parallel line. We’ll do one two three four and it also occurs down here one two three four now each of these angles corresponds with the other angle of the same number. Angle one here will be equal to angle 1, angle two will be equal to angle 2, 3 & 3, 4 & 4. Now the case of this X here this X is located at angle 3 which means that angle 3 down here will also be identical or congruent to that whatever angle is here. Now in the case of X, X is 60 and because it corresponds to Y that means that Y also has to be 60 degrees. Try these practice problems and other by downloading the free parallel lines cut by transversal worksheet above.