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Math Geometry FAIM 2015 Form 1-B [1530459]StudentClassDate

InstructionsUse your Response Document to answer question 21.

1. In the figure below,  

Which relationship can be proven knowing that  

 A.

 B.

 C.

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 D.

2. is translated to form as shown on the coordinate plane.

What are the translations applied to  to form  

3. How many square inches is the area of parallelogram MNOP, shown on the coordinate plane below? 

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4.   Which statement must be true? 

 A.

 B.

 C.

 D.

5. Isabella graphed a quadrilateral with coordinates and  on a coordinate plane.

Part A. Use the coordinates of the points to prove that WXYZ is a parallelogram.

Part B. Isabella thinks that quadrilateral WXYZ is a also rectangle. Is she

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correct? Explain.

Use words and/or numbers to show your work. 

6. Dwayne considers a square drawn in the xy-coordinate plane with vertices

Dwayne finds squa

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re

by dilating TUVW with a scale factor of 2, and with a center of dilation at

What is the slope of

  A.

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 B.

 C.

 D.

7. Alex needs to bisect

using a compass and straightedge. He starts by perfo

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rming the following steps.

Step 1: Place the compass on vertex B of the angle.Step 2: Draw an arc that intersects bo

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th sides of the angle.Step 3: Label these intersections as point D and point E.Step 4: Place the compass at poi

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nt D and draw an arc in the interior of the angle.

What are the next steps Alex should take in his construction?

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  A. Adjust the compass width to be half the distance between pointBand pointEand then place the

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compass on pointEand draw an arc in the interior of the angle that crosses the other arc. 

  B. Withou

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t adjusting the compass width, place the compass at pointEand draw an arc in the interior of the angle

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that crosses the other arc. 

  C. Adjust the compass width to be half the distance between pointB

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and pointEand then place the compass on pointEand draw an arc on the exterior of the angle. 

  D. Wi

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thout adjusting the compass width, place the compass at pointEand draw an arc on the exterior of the

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angle that is opposite the other arc.  

8. Given points 

and

what is the value of the ratio

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9. Kayla measured the distances surrounding a lake, as shown in the diagram below.

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Kayla used the diagram to determine the distance across the lake. If 

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what is the distance across the lake?  

 A. 75

ft 

 B. 95

ft 

C. 112.5 ft 

D. 165.8 ft 

10.

Quadrilateral AB

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CD is considered a cyclic quadrilateral because there is a circle passing through all four of its vertices.

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What is the sum, in degrees, of

Explain your answer.

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11.

Consider the diagram and angle measurements shown below. 

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What is

 A.

 B.

 C.

 D.

12.

A flat, rectangular television

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screen has a height of 25 inches and a diagonal of 32 inches. What is the width of the television screen? Round yo

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ur answer to the nearest hundredth of an inch. 

13.

The figure below shows the circles and

Which of thes

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e statements can be used to prove that the circles are similar? 

  A. Th

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e circles and

are similar because

can be mapped onto

by a translation two units to the right an

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d three units up followed by a dilation about its center by a scale factor of

  B. The circles and

are

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similar because

can be mapped onto

by a translation two units to the right and three units up followed

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by a dilation about its center by a scale factor of 2. 

  C. The circles and

are similar because

can

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be mapped onto

by a translation two units to the left and three units down followed by a dilation about its

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center by a scale factor of

  D. The circles and

are similar because

can be mapped onto

by

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a translation two units to the left and three units down followed by a dilation about its center by a scale fac

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tor of 2. 

14.

In the figure below,

  Write a proportion using the sid

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e lengths of the triangles that can be used to prove that

15.

Part A. A cone is carved from a cylinder

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so that the cone has a volume of

 and a diameter of 4 ft. If the cylinder has the same height and base as the co

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ne, find the height and the volume of the cylinder. Show your work.

Part B. A cone is carved from a cylinder. If

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the cylinder has the same height and base as the cone, explain how to determine the volume of the cylinder wit

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hout determining the height or the size of the base.

Use words and/or numbers to show your work. 

16 In

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. the figure below, Circle C has tangent lines

and 

and diameter

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Angle QSR measures

What is the measure of

 A.

  B.

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 C.

 D.

17.

In the diagram below,

What is the

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most precise classification for quadrilateral ADEF? 

18.

The radius and slant height of a right cone are 3 cm an

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d 5 cm, respectively. To the nearest tenth of a cubic centimeter, what is the volume of the cone? 

19.

The

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figure below shows isosceles triangle ABC, with 

and

bisecting

Which is a valid

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proof that shows

? 

A.

B.

C.

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D.

20.

Soda cans are made out of aluminum and are shaped like a cylinder. The formula for the

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surface area of a cylinder can be used to find the amount of aluminum, in square centimeters, that is needed to ma

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ke a soda can. The formula is provided below:

A typical soda can measures 12 centimeters tall and has a vol

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ume of 235.5 cubic centimeters. To the nearest whole number, how many square centimeters of aluminum are require

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d to make a can? 

A. 39 square centimeters 

B. 188 square centimeters 

  C. 208 square centimeters

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D. 228 square centimeters 

21.

Mark is planting a garden in a corner of his backyard. He wants to divide the

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garden into different sections for different vegetables, and he wants the sections to be congruent to each ot

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her so that he is sure that the different types of plants have the same amount of space.  

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 Part A. Sketch one segment that would divide the garden to produce two co

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ngruent triangles.   Part B. Use a paragraph proof to explain how you know that the two triangles are co

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ngruent. Part C. Now, Mark wants to divide each of the two triangular sections in half so the garden will ha

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ve a total of four congruent triangles. Sketch one possible way Mark can do this, and label the side lengths an

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d angle measures. Part D. Explain how you know that all four triangles are congruent, using a paragraph

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proof and a different congruence postulate than used in part A. Part E. How does the side length of the ori

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ginal garden relate to the side length of the four small triangles? Explain, using a paragraph proof and geometric

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postulates to support your answer.   Place an "X" in the answer box below.Answer the question on the Resp

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onse Document provided.Click next. 

22.

What is the center of a circle given by the equation:

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23.

Line segment

is drawn in the first quadrant. Its image, line segment

is formed by reflecting

ov

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er the x-axis. Which statement will always be true? 

  A. Line segments

and

are parallel to each othe

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r. 

B. Line segments

and

are perpendicular to each other. 

  C. Corresponding points on

and

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are equidistant from the xaxis. 

  D. Corresponding points on

and

can be connected to form a

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line segment perpendicular to both

and

24.

Which words correctly complete the statement below?

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is dilated with the center of dilation at the origin and a scale factor of 0.5 to obtain

The triangles’ corresponding

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angles are

and their corresponding sides are

therefore, the triangles are

  A. congruent; proport

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ional; similar 

B. congruent; congruent; congruent 

C. proportional; proportional; similar 

  D. proport

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ional; congruent; congruent 

25.

What is the y-intercept of the line perpendicular to the line

th

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at includes the point

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