Version A
Geometry - Unit 8 Assessment- Similarity
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
____1.The SearsTower in Chicago is 1450 feet high. A model of the tower is 24 inches tall. What is the ratio of the height of the model to the height of the actual SearsTower?
a. / 1 : 725 / b. / 725 : 1 / c. / 12 : 725 / d. / 725 : 12____2.The length of a rectangle is inches and the width is inches. What is the ratio, using whole numbers, of the length to the width?
a. / 26 : 15 / b. / 26 : 30 / c. / 15 : 26 / d. / 13 : 15____3.If then 3a = ____.
a. / 3b / b. / 10b / c. / 5b / d. / 6b____4.If , then = ____.
a. / / b. / / c. / / d. /Solve the proportion.
____5.
a. / / b. / 5 / c. / / d. / 25____6.On a blueprint, the scale indicates that 6 cm represent 15 feet. What is the length of a room that is 9 cm long and 4 cm wide on the blueprint?
a. / 22.5 ft / b. / 1.5 ft / c. / 6 ft / d. / 16.5 ft____7.Figure . Name a pair of corresponding sides?
a. / / b. / / c. / / d. /____8.Determine whether the figures are similar.
a. / similarb. / not similar
c. / not enough information
Are the polygons similar? If they are, write a similarity statement and give the similarity ratio.
____9.In RST, RS = 10, RT = 15, and mR = 32. In UVW, UV = 12, UW = 18, and mU = 32.
a. / ; / c. / ;b. / ; / d. / The triangles are not similar.
____10.ABCD ~ WXYZ. AD = 6, DC = 3, and WZ = 59. Find YZ. The figures are not drawn to scale.
a. / 118 / b. / 29.5 / c. / 21.7 / d. / 177The polygons are similar, but not necessarily drawn to scale. Find the values of x and y.
____11.The pentagons are similar.
a. / x = 27, y = 4 / c. / x = 28, y = 5b. / x = 27, y = 5 / d. / x = 28, y = 4
____12.Are the triangles similar? If so, explain why.
a. / yes, by SAS / b. / yes, by SSS / c. / yes, by AA / d. / no____13. What is the measure of ?
a. / 70 / b. / 110 / c. / 250 / d. / 35State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used.
____14.In QRS, QR = 16, RS = 64, and mR = 29. In UVT, VT = 8, TU = 32, and mT = 29.
a. / ; ASA / c. / ; ASAb. / ; ASA / d. / The triangles are not similar.
____15.
a. / ; SSS / c. / ; AAb. / ; SAS / d. / The triangles are not similar.
____16.
a. / ; SAS / c. / ; SSSb. / ; SAS / d. / The triangles are not similar.
STUDENT PRODUCE RESPONSE
____17.Michele wanted to measure the height of her school’s flagpole. She placed a mirror on the ground 48 feet from the flagpole, then walked backwards until she was able to see the top of the pole in the mirror. Her eyes were 5 feet above the ground and she was 12 feet from the mirror. Using similar triangles, find the height of the flagpole to the nearest tenth of a foot.
____18.Find the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale.
Solve for x.
____19.
____20.
____21.
The figures are similar. The area of one figure is given. Find the area of the other figure to the nearest whole number.
____22.The area of the smaller trapezoid is 558 m.
ESSAY
23.Write a proof.
Given:
Prove:
24.The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments of length a and b. Describe how to find the area of the triangle in terms of a and b. Show your work.
Geometry Unit 8 Assessment ID: A
Answer Section
MULTIPLE CHOICE
1.ANS:ADIF:L1REF:8-1 Ratios and Proportions
OBJ:8-1.1 Using Ratios and Proportions
STO:MD 3.12.4b, MD 7.10, MD 7.12, MD 8.6, MD 9.3, MD 10.3
TOP:8-1 Example 1KEY:ratio,word problem
MSC:NAEP N4c, CAT5.LV20.46, CAT5.LV20.54, CAT5.LV20.55, IT.LV16.CP, IT.LV16.FR, S9.TSK2.GM, S9.TSK2.NS, S10.TSK2.GM, S10.TSK2.NS, TV.LV20.10, TV.LV20.13
2.ANS:ADIF:L2REF:8-1 Ratios and Proportions
OBJ:8-1.1 Using Ratios and Proportions
STO:MD 3.12.4b, MD 7.10, MD 7.12, MD 8.6, MD 9.3, MD 10.3
TOP:8-1 Example 1KEY:ratio
MSC:NAEP N4c, CAT5.LV20.46, CAT5.LV20.54, CAT5.LV20.55, IT.LV16.CP, IT.LV16.FR, S9.TSK2.GM, S9.TSK2.NS, S10.TSK2.GM, S10.TSK2.NS, TV.LV20.10, TV.LV20.13
3.ANS:CDIF:L1REF:8-1 Ratios and Proportions
OBJ:8-1.1 Using Ratios and Proportions
STO:MD 3.12.4b, MD 7.10, MD 7.12, MD 8.6, MD 9.3, MD 10.3
TOP:8-1 Example 2KEY:proportion,Cross-Product Property
MSC:NAEP N4c, CAT5.LV20.46, CAT5.LV20.54, CAT5.LV20.55, IT.LV16.CP, IT.LV16.FR, S9.TSK2.GM, S9.TSK2.NS, S10.TSK2.GM, S10.TSK2.NS, TV.LV20.10, TV.LV20.13
4.ANS:CDIF:L2REF:8-1 Ratios and Proportions
OBJ:8-1.1 Using Ratios and Proportions
STO:MD 3.12.4b, MD 7.10, MD 7.12, MD 8.6, MD 9.3, MD 10.3
TOP:8-1 Example 2KEY:Cross-Product Property,proportion
MSC:NAEP N4c, CAT5.LV20.46, CAT5.LV20.54, CAT5.LV20.55, IT.LV16.CP, IT.LV16.FR, S9.TSK2.GM, S9.TSK2.NS, S10.TSK2.GM, S10.TSK2.NS, TV.LV20.10, TV.LV20.13
5.ANS:DDIF:L1REF:8-1 Ratios and Proportions
OBJ:8-1.1 Using Ratios and Proportions
STO:MD 3.12.4b, MD 7.10, MD 7.12, MD 8.6, MD 9.3, MD 10.3
TOP:8-1 Example 3KEY:proportion,Cross-Product Property
MSC:NAEP N4c, CAT5.LV20.46, CAT5.LV20.54, CAT5.LV20.55, IT.LV16.CP, IT.LV16.FR, S9.TSK2.GM, S9.TSK2.NS, S10.TSK2.GM, S10.TSK2.NS, TV.LV20.10, TV.LV20.13
6.ANS:ADIF:L1REF:8-1 Ratios and Proportions
OBJ:8-1.1 Using Ratios and Proportions
STO:MD 3.12.4b, MD 7.10, MD 7.12, MD 8.6, MD 9.3, MD 10.3
TOP:8-1 Example 4KEY:proportion,Cross-Product Property,word problem
MSC:NAEP N4c, CAT5.LV20.46, CAT5.LV20.54, CAT5.LV20.55, IT.LV16.CP, IT.LV16.FR, S9.TSK2.GM, S9.TSK2.NS, S10.TSK2.GM, S10.TSK2.NS, TV.LV20.10, TV.LV20.13
7.ANS:DDIF:L1REF:8-2 Similar Polygons
OBJ:8-2.1 Similar PolygonsSTO:MD 2.12.5a, MD 2.12.2b, MD 7.12, MD 9.8, MD 10.3
TOP:8-2 Example 1KEY:similar polygons,corresponding sides
MSC:NAEP G2e, NAEP M1k, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.52
8.ANS:BDIF:L1REF:8-2 Similar Polygons
OBJ:8-2.1 Similar PolygonsSTO:MD 2.12.5a, MD 2.12.2b, MD 7.12, MD 9.8, MD 10.3
TOP:8-2 Example 2KEY:similar polygons
MSC:NAEP G2e, NAEP M1k, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.52
9.ANS:BDIF:L1REF:8-2 Similar Polygons
OBJ:8-2.1 Similar PolygonsSTO:MD 2.12.5a, MD 2.12.2b, MD 7.12, MD 9.8, MD 10.3
TOP:8-2 Example 2
KEY:similar polygons,corresponding sides,corresponding angles
MSC:NAEP G2e, NAEP M1k, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.52
10.ANS:BDIF:L1REF:8-2 Similar Polygons
OBJ:8-2.1 Similar PolygonsSTO:MD 2.12.5a, MD 2.12.2b, MD 7.12, MD 9.8, MD 10.3
TOP:8-2 Example 3KEY:corresponding sides,proportion
MSC:NAEP G2e, NAEP M1k, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.52
11.ANS:ADIF:L2REF:8-2 Similar Polygons
OBJ:8-2.1 Similar PolygonsSTO:MD 2.12.5a, MD 2.12.2b, MD 7.12, MD 9.8, MD 10.3
TOP:8-2 Example 3KEY:corresponding sides,proportion
MSC:NAEP G2e, NAEP M1k, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.52
12.ANS:CDIF:L1REF:8-3 Proving Triangles Similar
OBJ:8-3.1 The AA Postulate and the SAS and SSS Theorems
STO:MD 2.12.5a, MD 8.2, MD 8.3, MD 8.5, MD 9.6, MD 10.3
TOP:8-3 Example 2
KEY:Angle-Angle Similarity Postulate,Side-Side-Side Similarity Theorem,Side-Angle-Side Similarity Theorem
MSC:NAEP G2e, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14
13.ANS:ADIF:L2REF:8-3 Proving Triangles Similar
OBJ:8-3.1 The AA Postulate and the SAS and SSS Theorems
STO:MD 2.12.5a, MD 8.2, MD 8.3, MD 8.5, MD 9.6, MD 10.3
TOP:8-3 Example 1KEY:Angle-Angle Similarity Postulate,corresponding angles
MSC:NAEP G2e, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14
14.ANS:DDIF:L1REF:8-3 Proving Triangles Similar
OBJ:8-3.1 The AA Postulate and the SAS and SSS Theorems
STO:MD 2.12.5a, MD 8.2, MD 8.3, MD 8.5, MD 9.6, MD 10.3
TOP:8-3 Example 2KEY:corresponding sides
MSC:NAEP G2e, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14
15.ANS:ADIF:L1REF:8-3 Proving Triangles Similar
OBJ:8-3.1 The AA Postulate and the SAS and SSS Theorems
STO:MD 2.12.5a, MD 8.2, MD 8.3, MD 8.5, MD 9.6, MD 10.3
TOP:8-3 Example 2KEY:Side-Side-Side Similarity Theorem
MSC:NAEP G2e, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14
16.ANS:ADIF:L1REF:8-3 Proving Triangles Similar
OBJ:8-3.1 The AA Postulate and the SAS and SSS Theorems
STO:MD 2.12.5a, MD 8.2, MD 8.3, MD 8.5, MD 9.6, MD 10.3
TOP:8-3 Example 2KEY:Side-Angle-Side Similarity Theorem,corresponding sides
MSC:NAEP G2e, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14
17.ANS:= 20 ftDIF:L1REF:8-3 Proving Triangles Similar
OBJ:8-3.2 Applying AA¸ SAS¸ and SSS Similarity
STO:MD 2.12.5a, MD 8.2, MD 8.3, MD 8.5, MD 9.6, MD 10.3
TOP:8-3 Example 4KEY:Angle-Angle Similarity Postulate,word problem
MSC:NAEP G2e, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14
18.ANS:= √130DIF:L1REF:8-4 Similarity in Right Triangles
OBJ:8-4.1 Using Similarity in Right Triangles
STO:MD 2.12.2a, MD 2.12.2b, MD 2.12.5aTOP:8-4 Example 2
KEY:corollaries of the geometric mean,proportion
MSC:NAEP G2e, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.52
19.ANS:= 5DIF:L2REF:8-5 Proportions in Triangles
OBJ:8-5.1 Using the Side-Splitter TheoremSTO:MD 2.12.2b, MD 10.3
TOP:8-5 Example 1KEY:Side-Splitter Theorem
MSC:NAEP G2e, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.52
20.ANS:= 8DIF:L1REF:8-5 Proportions in Triangles
OBJ:8-5.1 Using the Side-Splitter TheoremSTO:MD 2.12.2b, MD 10.3
TOP:8-5 Example 2KEY:corollary of Side-Splitter Theorem
MSC:NAEP G2e, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.52
21.ANS:= 6DIF:L1REF:8-4 Similarity in Right Triangles
OBJ:8-4.1 Using Similarity in Right Triangles
STO:MD 2.12.2a, MD 2.12.2b, MD 2.12.5aTOP:8-4 Example 2
KEY:corollaries of the geometric mean,proportion
MSC:NAEP G2e, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.52
22.ANS:= 3147 m DIF:L1REF:8-6 Perimeters and Areas of Similar Figures
OBJ:8-6.1 Finding Perimeters and Areas of Similar Figures
STO:MD 2.12.2b, MD 3.12.3, MD 3.12.4b, MD 10.3TOP:8-6 Example 2
KEY:similar figures,area,trapezoid
MSC:NAEP M2g, NAEP N4c, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.52
ESSAY
23.ANS:
[4] / Answers may vary. Sample:1. / / Given
2. / / Prop. of Proportions
3. / / Vertical are .
4. / / SAS Theorem
[3] / correct steps but with minor error in reasons
[2] / error in steps
[1] / error in steps and reasons
DIF:L3REF:8-3 Proving Triangles Similar
OBJ:8-3.2 Applying AA¸ SAS¸ and SSS Similarity
STO:MD 2.12.5a, MD 8.2, MD 8.3, MD 8.5, MD 9.6, MD 10.3
KEY:extended response,rubric-based question,Property of Proportions,vertical angles,Side-Angle-Side Similarity Theorem
MSC:NAEP G2e, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14
24.ANS:
[4] / Answers may vary. Sample:The area of a triangle is given by . The base is (a + b). The height is found by using the proportion . So . Therefore, the area of the right triangle is .
[3] / correct methods with a minor computational error
[2] / error in method
[1] / correct answer but with no work shown
DIF:L3REF:8-4 Similarity in Right Triangles
OBJ:8-4.1 Using Similarity in Right Triangles
STO:MD 2.12.2a, MD 2.12.2b, MD 2.12.5a
KEY:corollaries of the geometric mean,area of a triangle,extended response,rubric-based question
MSC:NAEP G2e, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.52