Geometry and Trigonometry section of SAT

Quadrilateral P'Q'R'S' is similar to quadrilateral PQRS, where P, Q, R, and S correspond to P', Q', R', and S', respectively. The measure of angle P is 30°, the measure of angle Q is 50°, and the measure of angle R is 70°. The length of each side of P'Q'R'S' is 3 times the length of each corresponding side of PQRS. What is the measure of angle P'?

• 10°

• 30°

• 40°

• 90°

What is the area, in square centimeters, of a rectangle with a length of 34 centimeters (cm) and a width of 29 cm?

• 986 cm²

• 986 square centimeters

• 986

• 986 sq cm

• 5

• 7

• 10

• 14

A cylinder has a diameter of 8 inches and a height of 12 inches. What is the volume, in cubic inches, of the cylinder?

• 16π

• 96π

• 192π

• 768π

Which equation shows the relationship between the side lengths of the given triangle?

• 4b = 19

• 4 + b = 19

In the figure, line m is parallel to line n, and line k intersects both lines. Which of the following statements is true?

• The value of x is less than 145.

• The value of x is greater than 145.

• The value of x is equal to 145.

• The value of x cannot be determined.

• 97

• 145

• 441

• 113

The area of a rectangle is 57 square inches. The length of the longest side of the rectangle is 19 inches. What is the length, in inches, of the shortest side of this rectangle?

• 3 inches

• 4 inches

• 5 inches

• 6 inches

Triangle ABC is similar to triangle XYZ, such that A, B, and C correspond to X, Y, and Z respectively. The length of each side of triangle XYZ is 2 times the length of its corresponding side in triangle ABC. The measure of side AB is 16. What is the measure of side XY?

• 14

• 16

• 18

• 32