Vertex Angle of an Isosceles Triangle

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  • 0:02 Real-Life Triangles
  • 0:26 Isosceles Triangles
  • 0:53 The Vertex Angle
  • 1:25 Measuring the Vertex Angle
  • 2:37 Practice Problem
  • 3:35 Lesson Summary
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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.

Real-Life Triangles

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

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!

The Vertex Angle

Isosceles: 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.

Measuring the Vertex Angle

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°.

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