McGraw-Hill Education GRE 2019

For this question, indicate all the answer choices that apply.

If a triangle has side lengths of 4 and 7, which of the following could be the

length of the third side of the triangle?

A 3

B 4

C 5

D 9

E 11

F 13

SOLUTION: The third side of the triangle must be greater than (7 – 4) and less

than (7 + 4). Thus the length of the third side must be between 3 and 11. Of

the choices, the length could be 4, 5, or 9.

Basic Property 3: The greater the measurement of a triangle’s angle, the greater the

length of the corresponding side.

An angle’s corresponding side is the side opposite that angle. In the following

triangle, each angle’s corresponding side is indicated by the arrows. Note that this

relationship also works in reverse: the greater the length of a side, the greater the

measurement of the corresponding angle. It is also important to note that this

information only provides a relationship between the corresponding sides and

angles of a triangle. Without additional information, you cannot infer how much

greater one side or angle is than another side or angle.

100° > 50° > 30°

AB > AC > BC

A C

B

30° 100°

50°

Isosceles Triangles

An isosceles triangle is any triangle that has two equal angles. Since the two angles

are equal, the corresponding sides will also be equal. Thus as you saw with the

Basic Property 3, the relationship works in reverse. If a triangle has two equal sides,

it will be isosceles, and the angles opposite those sides will be equal.

x° x°

B

A C

BC = AB

∠A = ∠C

CHAPTER 13 ■ GEOMETRY 377

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