4/5/2016 USATestprep, Inc. http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=547 1/18 Grade 8 Mathematics EOG (GSE) Quiz Answer Key Expressions and Equations - (MGSE8.EE.6 ) Use Similar Triangles Student Name: _______________________ Date: _________ Teacher Name: THUYNGA DAO Score: _________ 1) The quadrilaterals are similar. If CB = 6, GF = 3, and CD = 4, find GH. A) 2 B) 3 C) 8 D) 10 Explanation: The solution is 2. The side lengths in ABCD are twice as long as the side lengths in EFGH. 2) The triangles shown are similar. Which side corresponds to QR ? A) FE B) ED C) FD D) QP Explanation: The solution is FD . If you rotate triangle DEF so that it is oriented the same way as triangle PQR, you can see that QR corresponds to FD . 3)
Explanation:The solution is 3.5. The problem can be solved using the proportion:
2
1=
7
x
6)
The two figures have a scale of 3:1. What is the length of the corresponding side in the second figure?
A) 5
B) 15
C) 30
D) 45
Explanation:The correct answer is 5. With a scale of 3:1 that means that the first figure is 3 times bigger than the second. So take themeasurement of 15 and divide it by 3 to find the corresponding measurement.
The two figures shown are similar. Using the information given, find the length of segment JK.
A) 1
B) 2
C) 2.25
D) 8.25
Explanation:The correct length of JK is 2.25. Since these are similar figures you must set up a proportion with the known sides and the unknownsides. JK/ST = KL/TU, so JK = KL · ST/TU = 6 · 1.5/4 = 2.25
8)
Solve for AD.
A) 12
B) 10
C) 8
D) 6
Explanation:Solution: 8. To solve for AD, use the proportion 4/6=x/12, 6x = 48, x = 8.
Explanation:Solution: negativeA positive slope is an uphill line, a negative slope is a downhill line, zero slope is a horizontal line, and an undefined slope is avertical line; so the line graphed above is a downhill line so the correct answer is negative slope.
13)
What is the slope of the line?
A) -1
B) 0
C) 1
D) 20
Explanation:Solution: 0Since the line does not move vertically the rise is zero and the run is any number; the slope equals zero.
19) A rectangle has dimensions 7 ft x 12 ft. Which of the dimensions describe a rectangle that is similar to this rectangle?
A) 5 ft x 7 ft
B) 14 ft x 36 ft
C) 21 ft x 36 ft
D) 21 ft x 48 ft
Explanation:21 ft x 36 ft. The ratio of corresponding sides is 1:3.
20)
Pentagon JKLMN is similar to pentagon STUVW. If NJ = 4, WS = 3, and JK = 5, find ST.
A) 2.4
B) 3.75
C) 5.8
D) 6.7
Explanation:The length of ST is 3.75. This problem can be solved by matching up corresponding sides, setting up a proportion, and then solving.
21) An office building casts a 90 foot shadow. At the same time of day, a 5 foot woman standing near the building casts an 8 footshadow. What is the approximate height of the building to the nearest foot?
A) 40 feet
B) 49 feet
C) 56 feet
D) 63 feet
Explanation:The approximate height of the building is 56 feet. We can set up a proportion to solve this problem.
Which set of rectangles are similar to each other by a ratio of 2 : 5?
A) Set #1
B) Set #2
C) Set #3
D) Set #4
Explanation:Set #2 is two similar rectangles with a side ratio of 2 : 5.
28)
What does it mean if two figures are similar?
A) Similar figures have the same size and the same shape.
B) Similar figures have different sizes and different shapes.
C) Similar figures have the same size but are different shapes.
D) Similar figures have the same shape but are different sizes.
Explanation:Similar figures have the same shape but are different sizes. Figures that are the same size and the same shape are called congruentfigures.
Explanation:For shapes to be similar they must have the same shape but not necessarily the same size. Their sides need to be proportional toone another. Since circles just have one side (a radius) they are similar to one another.
