Using Congruent Properties Of Congruent Triangles To Find Values Explained

In this video we discuss how to use congruent properties of congruent triangles to find unknown values. We go through an example of this by finding the value of x

Transcript/notes
Here are 2 congruent triangles. We are given that triangle ABC is congruent to triangle JKL. This is written so the corresponding angles and corresponding sides are in the same order. And, since they are congruent, we know that corresponding angles and corresponding sides are congruent.
Here is a listing of the corresponding angles and corresponding sides.
Now lets say that we know angle A is 30 degrees, and angle C is 80 degrees. And we are also given that angle K equals 2x plus 30, degrees.

What is the value of x?

To find the value of x, we know that corresponding angles of congruent figures are congruent, which means that angle B is congruent to angle K, so, the measure of angle B equals the measure of angle K.

We also know that one of the properties of triangles is that all of the angles of a triangle sum up to 180 degrees, so, angle A, plus angle B, plus angle C equals 180 degrees, 30 degrees plus angle B, plus 80 degrees equals 180 degrees. From this, we find that angle B equals 70 degrees.

Since the measure of angle B equals the measure of angle K, we can set these equal to one another. 70 degrees equals 2x plus 30, degrees. And we get x equals 20.

When solving problems like these, where the congruent triangles are facing different directions, so to speak, it can be beneficial to list the corresponding angles and corresponding sides.

Chapters/Timestamps
0:00 Corresponding angles and sides of triangles
0:21 Example of finding a value for congruent triangles

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