Name:    RC2:  Triangles Geometry Simulation 2012

(Questions courtesy of Chesterfield County Public Schools)

Multiple Choice

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

1.

.
Which of the following statements is NOT true?
 a. b. c. d.

2.

In the following diagram, it is given that C is the midpoint of , that , and that .

Prove by selecting the most logical sequence of statements and reasons.
 a. 5. Perpendicular lines form four right angles6. All right angles are congruent7. Angle-Side-Angle (ASA) b. 5. Given6. All right angles are congruent7. Angle-Side-Angle (ASA) c. 5. Definition of congruent angles6. All right angles are congruent7. Side-Angle-Side (SAS) d. 5. Perpendicular lines form four right angles6. Alternate interior angles are congruent7. Right triangles are congruent to each other

3.

For what value of x is ?

 a. 2 b. 2.1 c. 2.5 d. 4.125

4.

Select all sets of given triangle lengths that would form a right triangle.

 I.     3, 4, 6 III.    11, 60, 61 V.     7, 24, 25 II.     8, 15, 17 IV.     5, 7, 12 VI.     12, 15, 18
 a. II, IV, V b. II, III, V c. I, V, VI d. IV only

5.

Which set of lengths could be the lengths of the sides of a triangle?
 a. 1, 2, 3 b. 6, 6, 14 c. 7, 24, 25 d. 10, 20, 33

6.

Roof trusses often use right triangles to make a flimsy 2 x 4 more rigid to hold up the weight of the roof. If a house is 40 feet wide and the roof is an isosceles triangle with base angles of 30 degrees, how far is it from the bottom edge of the roof to the peak?

 a. ft. b. ft. c. ft. d. 40 ft.

7.

On a map, Richmond, Danville, and Charlottesville form a triangle.  Charlottesville is 85 miles from Richmond and Danville is 100 miles from Richmond. Which is a possible distance between Danville and Charlottesville?
 a. 5 miles b. 15 miles c. 150 miles d. 185 miles

8.

In scalene triangle ABC, and .  What is the order of the sides in length, from longest to shortest?
 a. b. c. d.

9.

Pedro has a square practice net in his backyard.  The diagonal of the net is 6 feet.   Find the length of one side of the net.
 a. feet b. feet c. 3 feet d. 12 feet

10.

A surveyor is trying to determine the width of a river.  He first stands at point A, directly opposite a tree at point B.  He then walks 100 feet to point C.  He measures the acute angle at point C to be 79°.  What is the width, w, of the river?

 a. 19.4 feet b. 101.87 feet c. 514.5 feet d. 524.1 feet

11.

From the top of a 210 foot tall lighthouse, the angle of depression to a boat is .  Find the distance from the boat to the base of the lighthouse.

 a. 95.3 feet b. 107 feet c. 187.1 feet d. 412.1 feet

12.

and point E are shown in the diagram below.

Determine a possible location of point D to make.
 a. (2, 2) b. (4, 1) c. (3, 1) d. (4, 2)

13.

Given quadrilateral ABCD, where , , and a diagonal . Which method can be used to prove?
 a. Angle-Angle-Side (AAS) b. Side-Side-Angle (SSA) c. Side-Angle-Side (SAS) d. Side-Side-Side (SSS)

14.

Scott wants to swim across a river that is 400 meters wide.  He begins swimming perpendicular to the shore he started from but ends up 100 meters down river from where he started because of the current. How far did he actually swim from his starting point?
 a. 300 m b. 387.3 m c. 412.3 m d. 500 m