McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
5. Isosceles and Equilateral Triangles
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Exercise 47 Page 381

Consider the Triangle Sum Theorem to interpret the measure of the vertex angle.

never true

Practice makes perfect

Let's consider the given statement.

If the measures of the base angles of an isosceles triangle are integers, then the measure of its vertex angle is odd.

To evaluate the statement, let's draw a triangle with a vertex angle of v ^(∘) and base angles of b ^(∘).

By the Triangle Sum Theorem, we can find the measure of the vertex angle.

v+b+b=180
v+2b=180
v=180-2b

In this equation, m∠ v=180-2b. If the base angles are integers, the value of 2b will be even. Since the difference of two even numbers is even, the measure of the vertex angle will also be an even number. Therefore, the given statement is never true.

Extra

Isosceles Triangle
An isosceles triangle is a triangle that has two congruent sides called legs. The angle between these two sides is called the vertex angle and its opposite side is called the base. The angles formed by the legs and the base are called base angles. Base angles are congruent.

More information about isosceles triangles can be found on the following pages.