McGraw-Hill Education GRE 2019

Right Triangles

The GRE’s favorite shape is a right triangle. A right triangle is any triangle that

has a 90-degree angle. The 90-degree angle is formed at the intersection of the two

shorter sides, which are called the legs. The side opposite the 90-degree angle is the

longest side of a right triangle. It is called the hypotenuse.

Hypotenuse

Leg

Leg

The formula for the area of any triangle applies to right triangles, but in right

triangles, determining the area is easier than with other triangles. Why? Because

the base and height will simply be the two sides that form the 90-degree angle.

This is so because these two sides are perpendicular, meaning that one leg can

be considered the base and the other leg can be considered the height (it doesn’t

matter which leg you call the base and which leg you call the height).

A

BC

The area of the preceding triangle is 48. If the length of AB = 8, then what is

the length of BC?

SOLUTION: The area of a right triangle is^12 × (leg 1) × (leg 2). Substitute 8 for

(leg 1) and BC for leg 2:

48 =^12 × (8) × (BC)

48 = 4(BC)

12 = BC

The Pythagorean Theorem

Recall from Basic Property 3 that the greater the angle of a triangle, the longer

the corresponding side. Since the 90 degree angle in a triangle must be the largest

angle of the triangle, its corresponding side must be the longest side of the triangle.

This side is called the hypotenuse. The two sides forming the 90 degree angle are

called the legs.

The Pythagorean theorem provides a relationship that always holds true

between the sides of a right triangle. If a = the length of one leg, b = the length of

the other leg, and c = the length of the hypotenuse, then:

a^2 + b^2 = c^2

380 PART 4 ■ MATH REVIEW

04-GRE-Test-2018_313-462.indd 380 12/05/17 12:04 pm