McGraw-Hill Education GRE 2019

A parallelogram has the following properties:

1. Opposite sides are equal.


2. Opposite angles are equal.


3. The area = base × height.


4. The diagonal of a parallelogram creates two equivalent triangles.


5. Adjacent angles add up to 180.

A D

B C

a°d°

b° c°

In the parallelogram above, a = 2b. What is c?

SOLUTION: From Property 4, you know that a + b = 180. Substitute 2b for a:

2 b + b = 180

3 b = 180

b = 60

a = 120

From Property 2, you know that a = c. Thus c = 120.

Rectangles and Squares

A rectangle is a special type of parallelogram in which all angles equal 90 degrees.

The area of a rectangle is l × w. The perimeter of a rectangle is 2(l + w).

A square is a special type of rectangle in which all sides are equal. The area of a

square = s^2 (where s = the length of a side). The perimeter of a square is 4s (where

s = the length of a side).

Rectangle Square

What is the area of a square that has a perimeter of 20?

SOLUTION: Let s = the length of a side of the square. Thus

4 s = 20

s = 5

The area of the square is 5^2 = 25.

398 PART 4 ■ MATH REVIEW

04-GRE-Test-2018_313-462.indd 398 12/05/17 12:04 pm