McGraw-Hill Education GRE 2019

5. A Since lines 1 and 2 intersect to the left of the diagram, they are not parallel.
   As they converge, the angles closer to them become smaller. Thus a > c, and
   b > d. Since a and c are supplementary and b and d are supplementary, a and c
   must each be greater than 90. Thus their sum must be greater than 180.

Triangles

Triangles are the GRE’s favorite shape. They appear not only in questions that

explicitly ask you about triangles, but also in disguised form on questions

addressing other polygons, such as squares or rectangles. As you may recall from

high school, there are numerous properties associated with triangles. Let’s look

below at the properties you need to master for the GRE.

a° c°

b°

Basic Properties of Triangles

Basic Property 1: The sum of the internal angles in a triangle equals 180. Thus in the

preceding diagram, a + b + c = 180.

x° z°

y°

In the figure above, x = y = 2z. What is x?

SOLUTION: Since x, y, and z are the interior angles of a triangle, x + y + z = 180.

Use the given information to express all variables in terms of z:

2 z + 2z + z = 180

5 z = 180

z = 36

Since x = 2z, x = 2(36) = 72.

Basic Property 2: The length of any given side of a triangle must be greater than

the difference of the other two side lengths and less than the sum of the other two

side lengths.

376 PART 4 ■ MATH REVIEW

04-GRE-Test-2018_313-462.indd 376 12/05/17 12:04 pm