Geometry—Lesson 4 Examination
Please read these instructions before you begin to answer the questions that follow.
Write your answers and your work on this examination. When you are satisfied that your answers are correct, write them on the Answer Sheet found right after the exam. Then send the Answer Sheet only (not the exam itself) to Keystone National High School for grading. Attach separate paper for your work if necessary. Good Luck!
Solve using cross multiplication.
Determine whether the pair of triangles are similar. If they are similar, state the similarity postulate or theorem.
Find the geometric mean between 5 and 12.
At Oceanview High School, there are 360 students and 39 teachers. What is the ratio of students to each teacher, rounded to the nearest tenth?
a. 1: 9.2 c. 9.2 : 1
b. 120 : 13 d. 13: 120
Solve the proportion 𝑤+1 = 43
𝑤−1 31
a. 43/31 c. 6/37
b. 31/43 d. 37/6
Determine which pair of triangles are similar. Justify your answer. If they are similar, write the similarity statement.
yes, 𝛥ABC~𝛥FED by AA Similarity
yes, ΔABC~ΔDEF by AA Similarity
yes, ΔABC~ΔFDE by ASA Similarity
No, there is not enough information to determine similarity
Find the value of x and the length of AB.
a. x = 1.5, AB = 6 c. x = 1.5, AB = 3
b. x = 14/3, AB = 28/3 d. x = 14/3, AB = 28
The hypotenuse of a 30-60-90-degree right triangle has a measure of 10. What is the measure of the shortest side?
For questions 9 and 10, use the following triangle.
If b = 12, find c.
If b = 3, find a.
If ABCD ~ EFGH, find the value of x.
a. 18.75 c. 20
b. 22.75 d. 28
If ΔPQR ~ ΔSTU, find the value of x.
a. 4.4 c. 7
b. 24.6 d. 35
Mildred is flying a kite on a 30 m string. The angle of elevation of the kite measures 40 degrees, and Mildred’s hand is 2 m above the ground. About how high is the kite off the ground?
a. 21.3 m c. 19.3 m
b. 25 m d. 23 m
Solve using cross multiplication.
Determine whether the pair of triangles are similar. If they are similar, state the similarity postulate or theorem.
Find the geometric mean between 1 and 7.
In questions 17-20, determine if the given measures are sides of a right triangle.
17. 8, 6, 10
18. 9, 12, 15
19. 1.6, 3.2, 2.4
20. 9, 10, 11
The perimeter of a square is 32 cm. Find the length of a diagonal.
For questions 22-25, use the following triangle.
Find sin C.
a. c.
d.
Find cos C.
a. c.
d.
Find tan C.
a. c.
d.
Find tan A.
a. c.
d.
For questions 26 and 27, use the following diagram.
Find b.
Find a.
Solve using cross multiplication.
A 6-ft fence casts a shadow of 10 ft. At the same time a tree casts a shadow of 22 ft. How tall is the tree?
a. 2.7 ft c. 13.2 ft
b. 8.8 ft d. 132 ft
Find the geometric mean between 8 and 25.
The length of a rectangle is 2 cm and the width is 3 cm. Find the length of the diagonal.
The perimeter of an equilateral triangle is 18. Find the measure of the altitude.
a. 3 c. 3√2
b. 6 d. 3√3
A forest ranger spots a forest fire from the top of a lookout tower. The tower is 150 m tall, and the angle of depression to the fire is 10 degrees. About how far is the fire from the foot of the tower? Round to the nearest meter.
a. 148 m c. 863 m
b. 753 m d. 851 m
Three pounds of apples costs $1.09. How much will 11 pounds of apples cost? Round to the nearest cent.
Identify the hypotenuse in the right triangle below.
a. c.
b. d.
For questions 36-38, refer to the following triangle.
If e = 10 and f = 5, find d.
If f = 4 and c = 12, find a.
If c = 6, and d = 5, find e.
In the triangle below, find the value of z.
a. 3.2 c. 1
b. 39 d. 9.75
For questions 40-42, use the following triangle.
If a = 12, find b.
a. 12 c. 12√2
b. 6√2 d. 12√3
If b = 2, find c.
a. 2 c. 2√2
b. √2 d. 2√3
If c = 12, find a.
a. 12 c. 12√2
b. 6√2 d. 12√3
A plane’s altitude is 3,000 ft. For the pilot, the angle of depression of the base of a control tower is 15 degrees. To the nearest foot, what is the distance from the pilot to the base of the control tower?
a. 3,106 ft c. 11,198 ft
b. 11,591 ft d. 4,346 ft
A car traveled 100 miles in 2 hours. How many miles will it travel in 7 hours going at the same rate?
Your uncle is making you a desk for you to take to college. One side of the desk is 32 inches and the diagonal length is 36 inches. What is the length of the other side of the desk?
13.5 inches c. 27.2 inches
17.4 inches d. 16.5 inches
What is the equation for the Law of Cosines?
a. a2 = b2 + c2 – 2(b)(c)(cos A) c. b2 = a2 + c2 – 2(a)(c)(cos B)
b. c2 = a2 + b2 – 2(a)(b)(cos C) D. all of the above
Find the length of
a. 64.34 c. 8.02
b. 7.99 d. 5.55
Write an equation that could be used to find the value of y.
a. c.
b. d.
Find the m<C.
a. 60 c. 30
b. 75 d. 73
Find the m<T.
a. 40.5 c. 38.5
b. 139.5d. 124.5
