McGraw-Hill Education GRE 2019

This information is helpful because when you are working with an isosceles

triangle, you can assign the same variable to different angles or sides.

x°

X

z°

Z

y°

Y

In the figure above, side YZ = side XY. If x = 2y, then y =?

SOLUTION: Since YZ and XY are equal, their corresponding angles must be

equal. Thus x = z. The sum of the interior angles of a triangle is 180,

so x + x + y = 180. Substitute 2y for x:

2 y + 2y + y = 180

5 y = 180

y = 36

However, from the fact that a triangle is isosceles, you cannot necessarily infer

which sides or angles are equal.

40°

A C

B

triangle ABC is isosceles

QUANTITY A QUANTITY B

The measure of angle C 40

SOLUTION: Since triangle ABC is isosceles, it is possible that angle C = 40, in

which case the two quantities are equal. However, it can also be the case

that angle B = 40 and angle C = 100, in which case angle C > 40. Thus, the

relationship cannot be determined. The answer is D.

Equilateral Triangles

An equilateral triangle is a triangle in which all angles are equal and all sides are

equal. Since the angle measurements are the same and their sum is 180, each angle

in an equilateral triangle measures 60 degrees.

60°

A

60°

C

60°

B

BC = AC = AB

∠A = ∠B = ∠C

378 PART 4 ■ MATH REVIEW

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