McGraw-Hill Education GRE 2019

(singke) #1
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

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