COMPASS Geometry 3

Question 1

In a right triangle, the two legs measure 5 and 12. What is the length of the hypotenuse?

Accepted Answer

13

Answer

By the Pythagorean theorem: c = √(5² + 12²) = √(25 + 144) = √169 = 13.

Question 2

What is the area of a trapezoid with bases of length 6 and 10 and a height of 4?

Accepted Answer

32

Answer

Area = ½(b₁ + b₂) × h = ½(6 + 10) × 4 = ½ × 16 × 4 = 32.

Question 3

A tangent line to a circle:

Accepted Answer

Touches the circle at exactly one point

Answer

A tangent line touches a circle at exactly one point and is perpendicular to the radius drawn to that point.

Question 4

The exterior angle of a triangle equals:

Accepted Answer

The sum of the two non-adjacent interior angles

Answer

The Exterior Angle Theorem states that an exterior angle equals the sum of the two remote (non-adjacent) interior angles.

Question 5

A cylinder has a radius of 3 and a height of 7. What is its volume?

Accepted Answer

63π

Answer

Volume of a cylinder = πr²h = π(3²)(7) = π(9)(7) = 63π.

COMPASS Practice Test