WORKSHEET ON GEOMETRY FOR SAT

Identify the choice that best completes the statement or answers the question.

Problem 1 :

If the measure of one of the angles in a parallelogram is z, what is the measure of an adjacent angle?

a. 180 - z      b. 360 - 2z    c. 360 - z    d. 180 - z/2

e. z

Solution

Problem 2 :

In the figure below, the measure of ∠A is 60°. If the measure of ∠B is twice the measure of ∠C, what is the measure of ∠C?

a. 120°   b. 40°    c. 90°       d. 80°      e. 20°

Solution

Problem 3 :

In the figure below, △QST is similar to △RSU. What is the length of RU?

a. 10       b. 3/16      c. 64/3       d. 12         e. 16/3

Solution

Problem 4 :

In the figure below, what is the value of y in terms of x?

a. x + 60       b. 2x       c. 300 - x      d. 120 - x       e. x

Solution

Problem 5 :

In △ABC below, if AC = 10, then AB is equal to 

a. 5√2          b. 8        c. 2√5        d. 10√2      e. 5

Solution

Problem 6 :

If one side of a triangle is three times as long as a second side, then the perimeter of the triangle could be:

a. 6x      b. 3x         c. 7x        d. 5x      e. 4x

Solution

Problem 7 :

In the figure below, ∠B and ∠D are right angles. What is the length of BC?

a. 2√6     b. 4√2       c. 2√2     d. 4√3      e. 2√3

Solution

Problem 8 :

A parallelogram with two congruent adjacent sides must be a:

a. trapezoid       b. isosceles trapezoid     c. rectangle

d. square         e. rhombus

Solution

Problem 9 :

In the figure below, line a is parallel to line b. Line c intersects both a and b with angles 1, 2, 3, 4, 5, 6, 7, and 8 as shown. Which of the following lists include all of the angles that are congruent to angle 6 ?

a. angles 5, 7, 3 and 1      b. angles 8, 4, and 3

c. angles 8, 4, and 2        d. angles 5, 7, and 3

e. angles 8, 7, and 4

Solution

Problem 10 :

In the figure below, which pair of angles are supplementary?

a. ∠3 and ∠7       b. ∠1 and ∠4        c. ∠5 and ∠7

d. ∠4 and ∠7       e. ∠2 and ∠5

Solution

Problem 11 :

In the figure below, KL||NM. What is the length of LN?

a. 10        b. 11        c. 12√2        d. 11

e. It cannot be determined from the given information.

Solution

Problem 12 :

In the figure below, quadrilateral PQRS is a parallelogram. If ∠SMR is a right angle, then x must be equal:

a. b        b. 90 + a        c. 90 - b     d. 90 + a - b

e. 90 - (a + b)

Solution

Problem 13 :

Equilateral triangle ABC is inscribed in circle X. What is the measure of arc AB?

a. 30°      b. 60°     c. 90°      d. 120°    e. 240°

Solution

Problem 14 :

In the figure below, △LMN is an equilateral triangle. If LM is 4 units long, how many units long is arc MN?

a. 8π/3    b. 4π/3    c. 2π/3    d. π/3    e. π

Solution