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Math for Kids23 chapters | 325 lessons

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Lesson Transcript

Instructor:
*Mark Boster*

You probably know what an angle is, but what is a vertex? Or for that matter, what is an isosceles triangle? And where is the vertex angle in an isosceles triangle? Don't know? That's okay. You are about to find out.

Tony and Pat made a shirt for their mother. It was beautiful. However, when Mom tried it on, the left sleeve went to her elbow, and the right sleeve went to her wrist. They tried again, but this time, the left sleeve was longer than the right sleeve. What to do? If Tony and Pat had remembered what they'd learned about isosceles triangles, this problem could have been solved.

**Isosceles triangles** are triangles that have two legs, or sides, of the same length. The third side of the triangle can either be longer or shorter than the other two. An easy way some people have found to remember the word isosceles is to say it or think of it as 'I saw some sleeves.' Say it fast and it sort of sounds like isosceles, huh?

Well, anyway, shirts have two sleeves. Both sleeves are the same length. So, I saw some sleeves!

There is a triangle drawn over this person in a lime green shirt. Yes, it's an isosceles triangle. It has two sides of the same length, like sleeves, and one of another length. The two equal sides of the isosceles triangle are also called **legs**. The third side of the isosceles triangle, the side not the same length as the other two, is called the **base**. Across from the base is the **vertex angle**, the angle formed by the two sides of the same length. In the diagram, the person's head is at the vertex of this isosceles triangle.

There are two ways that you can find the measurement of the vertex angle. As you may already know, the angles in all triangles total 180°. Let's take an isosceles triangle where each base angle is 75°. Since 75° + 75° = 150°, 150° of the triangle are accounted for. Since 180° - 150° = 30°, the vertex angle must be 30° so that the angles of the triangle total 180°.

The second way to find the measurement of the vertex angle is to use a protractor. When you line up a protractor with one of the sides of a triangle and the vertex angle with the center of the line on the protractor, you'll find the measurement of the angle. In this case, it's 120°.

If you know the measurement of the vertex angle, then you also can find the measurement of the other two angles because they have to be the same. Just take the measurement of the vertex angle and subtract it from 180°.

180° - 120° = 60°

Just divide that in half and you have each of the other two angles.

60° / 2 = 30°

Pretty easy, huh?

Okay, let's try one more problem together. If it'll help, draw and label your own picture of an isosceles triangle.

If angle *b* is 25° and is not the vertex angle, what is the angle of the vertex angle?

First, you need to know which angle is the vertex angle. It's the angle across from the base. You know it is the vertex angle because the two equal angles and sides extend from the base.

Now, since you know which angle is the vertex angle, you know that the other two angles are the same. Since angle *b* is 25°, so is angle *c.*

So, we know that 25° + 25° = 50°. Remember, all the angles of a triangle total 180°. Since angles *b* and *c* total 50°, we can subtract that from 180°.

180° - 50° = 130°

We are left with 130°. Where could that be? The vertex angle!

**Isosceles triangles** are triangles that have two sides of the same length and two equal angles. The angle across from the **base**, or at the third side of the triangle, is the **vertex angle**.

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Math for Kids23 chapters | 325 lessons

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