Name:______Date:______
Class:______
Benchmark #3: Unit Test Stretching and Shrinking
Use the following diagrams of the floor plans for a tree house before and after reduction and enlargement by a copier. (7.G.1)
- a. What is the scale factor from the original design to the enlarged design?______
b. What is the scale factor from the original design to the reduced design?______(2 points)
2.Explain how the perimeter of the enlarged design compares to the perimeter of the original design. (2 points)
3.Explain how the area of the reduced design compares to the area of the original design. (2 points)
4. The parallelograms below are similar
Find the length of side AB and the measure of angle E. Explain how you found your answer or show your work
(7.RP.2) a) side AB = ______(2 points)
b) angleE = ______(1 point) Explain:______
5.Use the diagram below to determine the height of the flagpole. Show your work (7.RP.2) (2 points)
6.Which of the following rectangles is similar to a 10 by 15 rectangle? Explain (7.G.1) (2 points)
7. Gerald wanted to find the height of the flagpole at the entrance to his school. He used a mirror and recorded some measurements on a drawing. What is the height of the flagpole? Show you work (7.G.1) (2 points)
8.Find the value of x in each pair of similar figures below. Show your work (7.G.1) (2 points)
x=
9. After traveling 70 m in its dive, the submarine is at a depth of 25 m. What will the submarine’s depth be if it continues its dive for another 110 m? Show your work (7.G.1) (2 points)
10. The following picture is in an 8 centimeter by 6 centimeter frame. (7.G.1) (2 points)
Can this frame be reduced to 6 centimeters by 4 centimeters without distorting the shape? Explain why or why not.
11.Below is a triangle and its image. (7.G.1) (3 points)
a.Which of these rules was used to make the image?
(2x, 2y)(x, 2y)(2x, y)(2x, 4y)(4x, 2y)
b.Are the triangle and its image similar? Explain.
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Name:______Date:______
Class:______
Unit Test Stretching and Shrinking
Answer Section
SHORT ANSWER
1.ANS:
The enlarged design is related to the original design by a scale factor of 2.
PTS:1DIF:L2REF:Stretching and Shrinking | Unit Test
OBJ:Investigation 3: Scaling Perimeter and Area
NAT:CC 7.G.A.1| CC 7.G.B.6| NAEP G2f| NAEP G2dTOP:Problem 3.1
KEY:similar figures | scale factors
2.ANS:
The reduced design is related to the original design by a scale factor of .
PTS:1DIF:L2REF:Stretching and Shrinking | Unit Test
OBJ:Investigation 3: Scaling Perimeter and Area
NAT:CC 7.G.A.1| CC 7.G.B.6| NAEP G2f| NAEP G2dTOP:Problem 3.1
KEY:similar figures | scale factors
3.ANS:
C. The perimeter of the nlarged figure is 12 units. The perimeter of the original is 6 units. So, .
PTS:1DIF:L2REF:Stretching and Shrinking | Unit Test
OBJ:Investigation 3: Scaling Perimeter and Area
NAT:CC 7.G.A.1| NAEP G2e| NAEP G2cTOP:Problem 3.1
KEY:similar | similar figures | stretching
4.ANS:
H. The area of the reduced figure is 0.5 square units. The area of the original is 2 square units. So, .
PTS:1DIF:L2REF:Stretching and Shrinking | Unit Test
OBJ:Investigation 3: Scaling Perimeter and Area
NAT:CC 7.G.A.1| NAEP G2e| NAEP G2cTOP:Problem 3.1
KEY:similar | similar figures | stretching
5.ANS:
a. SideAB is 4 because each side of parallelogram ABCD is 4 times the length of each side of parallelogram EFGH. Side AB corresponds with side EF of the smaller parallelogram, so since side EF is 1 unit long, side AB is 4 units long. Angle E is 30° because it corresponds with Angle A of the larger parallelogram.
b.
Since the parallelograms are similar, also.
OR
Since the paralellograms are similar, also.
c. SideEH of the smaller parallelogram corresponds with side AD of the larger parallelogram. The ratio can be written as or as . The first ratio tells us that the smaller parallelogram, EGFH, is the size of the larger parallelogram, ABCD. The second ratio tells us that the larger parallelogram, ABCD, is 4 times the size of the smaller parallelogram, EFGH.
PTS:1DIF:L2REF:Stretching and Shrinking | Unit Test
OBJ:Investigation 4: Similarity and Ratios
NAT:CC 7.RP.A.2| CC 7.RP.A.2a| CC 7.EE.B.4| CC 7.NS.A.3| CC 7.G.A.1 |CC 7.RP.2.c| CC 7.RP.3| CC 7.G.1| NAEP G2e| NAEP G2f TOP: Problem 4.3 | Problem 4.1 | Problem 4.2
KEY:ratio | equivalent ratio | similar figures | finding similar measures
6.ANS:
= so x = 12; The flagpole is 12 feet high.
PTS:1DIF:L2REF:Stretching and Shrinking | Unit Test
OBJ:Investigation 4: Similarity and Ratios
NAT:CC 7.RP.A.2c| CC 7.RP.A.3| CC 7.G.A.1| NAEP G2e| NAEP G2f| NAEP G3c
TOP:Problem 4.4KEY:shadow | similar | finding similar measures
7.ANS:
rectangle A
PTS:1DIF:L2REF:Stretching and Shrinking | Question Bank
OBJ:Investigation 4: Similarity and Ratios
NAT:CC 7.RP.A.2c| CC 7.RP.A.3| CC 7.G.A.1| NAEP G2e| NAEP G2f
TOP:Problem 4.2 Ratios Within Similar Triangles
KEY:ratio | equivalent ratio | similar figures
8.ANS:
The flagpole measures cm.
PTS:1DIF:L2REF:Stretching and Shrinking | Question Bank
OBJ:Investigation 4: Similarity and Ratios
NAT:CC 7.RP.A.2c| CC 7.RP.A.3| CC 7.G.A.1| NAEP G2e| NAEP G2f| NAEP G3c
KEY:mirror | similar | finding similar measures
9.ANS:
a.x = 12 cm
b.x = 3 cm
PTS:1DIF:L2
REF:Stretching and Shrinking | Additional Practice Investigation 3
OBJ:Investigation 3: Scaling Perimeter and Area
NAT:CC 7.G.A.1| CC 7.G.B.6| NAEP G2e| NAEP G2f
TOP:Problem 3.3 Scale Factors and Similar Shapes
KEY:scale factors | similar figures | finding similar measures
10.ANS:
a.2.5 m
b.about 0.33 m
PTS:1DIF:L2
REF:Stretching and Shrinking | Additional Practice Investigation 5
OBJ:Investigation 4: Similarity and Ratios
NAT:CC 7.RP.A.2c| CC 7.RP.A.3| CC 7.G.A.1| NAEP G2e| NAEP G2f| NAEP G3c
KEY:mirror | similar | finding similar measures
11.ANS:
a.approximately 64.29 m
b.approximately 107.14 m
c.560 m
PTS:1DIF:L2
REF:Stretching and Shrinking | Additional Practice Investigation 5
OBJ:Investigation 4: Similarity and Ratios
NAT:CC 7.RP.A.2c| CC 7.RP.A.3| CC 7.G.A.1| NAEP G2e| NAEP G2f| NAEP G3c
KEY:nested triangles | similar | finding similar measures
12.ANS:
a.No, the base and height of the frame cannot be multiplied by the same scale factor to get a 6 centimeter by 4 centimeter frame.
b.Yes, the base and height of the frame can be multiplied by to get a 4 centimeter by 3 centimeter frame.
PTS:1DIF:L2REF:Stretching and Shrinking | Unit Test
OBJ:Investigation 4: Similarity and Ratios
NAT:CC 7.RP.A.2c| CC 7.RP.A.3| CC 7.G.A.1| NAEP G2e| NAEP G2f
TOP:Problem 4.2 Ratios Within Similar Triangles
KEY:ratio | equivalent ratio | similar figures
13.ANS:
a.Triangle ABC and Triangle ADE are similar because the corresponding angles in both triangles are congruent and the corresponding ratios of the sides are equivalent.
b.AE = 12 units
c.BC = 5 units
PTS:1DIF:L2REF:Stretching and Shrinking | Unit Test
OBJ:Investigation 4: Similarity and Ratios
NAT:CC 7.RP.A.2c| CC 7.RP.A.3| CC 7.G.A.1| NAEP G2e| NAEP G2f
TOP:Problem 4.3 Using Similarities to Find Measurements
KEY:ratio | equivalent ratio | similar figures | finding similar measures
14.ANS:
a. side AC = 20, side AB = 16, angle E =65°.
b. 4
c.
d. The perimeter of triangle ABC is 4 times the perimeter of triangle DEF.
e. The area of triangle ABC is 16 times the area of triangle DEF.
PTS:1DIF:L2REF:Stretching and Shrinking | Check-Up 2
OBJ:Investigation 3: Scaling Perimeter and Area
NAT:CC 7.G.A.1| CC 7.G.B.6| NAEP G2e| NAEP G2f
TOP:Problem 3.3 Scale Factors and Similar Shapes
KEY:scale factors | similar figures | finding similar measures
15.ANS:
a. (2x, 2y)
b. They are similar, because all corresponding sides increased by a scale factor of 2 and corresponding angles are equal.
PTS:1DIF:L2REF:Stretching and Shrinking | Question Bank
OBJ:Investigation 2: Similar FiguresNAT:CC 7.G.A.1| CC 7.G.B.6| NAEP G2f| NAEP G2d
TOP:Problem 2.2 Changing a Figure's Size and LocationKEY:similar figures | scaling | translating