SAT Geometry

In the figure above, MQ and NR intersect at point P, NP = QP, and MP = PR. What is the measure, in degrees, of angle QMR? (Disregard the degree symbol when gridding your answer.)

• 30

• 40

• 50

• 60

In the figure shown, WZ and XY intersect at point Q. YQ = 63, WQ = 70, WX = 60, and XQ = 120. What is the length of YZ?

• 44

• 54

• 64

• 74

In triangles ABC and DEF, angles B and E each have measure 27 degrees and angles C and F each have measure 41 degrees. Which additional piece of information is sufficient to determine whether triangle ABC is congruent to triangle DEF?

• The measure of angle A

• The length of side AB

• The lengths of sides BC and EF

• No additional information is needed

In triangles LMN and RST, angles L and R each have measure 60 degrees, LN = 10, and RT = 30. Which additional piece of information is sufficient to prove that triangle LMN is similar to triangle RST?

• MN = 7 and ST = 7

• MN = 7 and ST = 21

• The measures of angles M and S are 70 and 60 degrees, respectively.

• The measures of angles M and T are 70 and 50 degrees, respectively.

The perimeter of an equilateral triangle is 624 centimeters. The height of this triangle is k√3 centimeters, where k is a constant. What is the value of k?

• 16

• 84

• 96

• 104

In the xy-plane, the graph of 2x^2 - 6x + 2y^2 + 2y = 65 is a circle. What is the radius of the circle?

• 5

• 6.5

• √40

• √50

A manufacturing company produces two sizes of cylindrical containers that each have a height of 50 centimeters. The radius of container A is 16 centimeters, and the radius of container B is 25% longer than the radius of container A. What is the volume, in cubic centimeters, of container B?

• 16000π

• 20000π

• 25000π

• 31250π