Now, let’s explore the magic of corresponding angles. When a transversal line crosses two parallel lines, it creates something special: corresponding angles. These angles are located on the same side of the transversal and in the same position for each line it crosses.
In simpler terms, the corresponding angles are congruent, that is, they have the same measure.
To spot the corresponding angles, look for the distinctive “F” formation (either forward or backward), highlighted in red, as shown in the image at the beginning of the article. In this example, the angles labeled “a” and “b” are corresponding angles.
In the main image above, angles “a” and “b” have the same angle. You can always find the corresponding angles by looking for the F formation (either forward or backward), highlighted in red. Here is another example in the image below.
In this diagram, line t is the transverse line. Lines a and b are the parallel lines. The angles labeled 1 and 5 are corresponding angles, as are 4 and 8, 2 and 6, and 3 and 7. That means their angles are equal.
Jleedev/Wikimedia Commons/CC BY-SA
John Pauly is a high school mathematics teacher who uses a variety of ways to explain corresponding angles to his students. He says that many of his students have difficulty identifying these angles on a diagram.
For example, it says to take two similar triangles, triangles that have the same shape but not necessarily the same size. These different shapes can be transformed. They may have been resized, rotated, or mirrored.
Here we see corresponding angles in triangles. The triangles are different, but their corresponding angles are the same.
Isipeoria~enwikibooks/WikimediaCommons/CC BY-SA
In certain situations, you can assume certain things about the corresponding angles.
For example, let’s take two shapes that are similar, meaning they have the same shape but not necessarily the same size. If two figures are similar, their corresponding angles are congruent (equal). That’s great, Pauly says, because it allows the figures to maintain the same shape.
It says to think of an image you want to include in a document:
“You know that if you resize the image you have to pull a certain corner. If you don’t, the corresponding angles will not be congruent; in other words, it will look crooked and disproportionate. This also works the other way around. If you’re trying “When making a scale model, you know that all the corresponding angles have to be equal (congruent) to obtain the exact copy you are looking for.”
Apply corresponding angles
In practical situations, corresponding angles are useful. For example, when working on projects such as building railways, skyscrapers or other structures, ensuring you have parallel lines is essential, and being able to confirm the parallel structure with two corresponding angles is one way to check your work.
You can use the corresponding angles trick by drawing a straight line that intercepts both lines and measuring the corresponding angles. If they are congruent, you have done well.
