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Geometry March Benchmark Subject: Mathematics, Grade: 10, Year Created: 2018
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1) Use the graph below to answer the question.
Which pair of transformations maps quadrilateral 1 exactly onto quadrilateral 2?
reflect it over the line = –3, then rotate it 90° counterclockwise about the originy
reflect it over the -axis, then rotate it 180° about the originx
rotate it 90° counterclockwise about point (–3, –3), then translate it 8 units to the right
translate it 8 units to the right, then reflect it over the line = –3y
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2) Use the trapezoid on the grid below to answer this question.
Marvin reflected this trapezoid over a line, but only 2 of the vertices changed position. Which line could Marvin have used forthe reflection?
-axisx
-axisy
= 1 (bluex line)
= 1 (redy line)
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3) The point (3, -2) is reflected across the line =1.x
What are the coordinates of the reflected point?
(-3, -2)
(-1, -2)
(3, 4)
(5, 2)
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4) Segments and are radii of circle . CY CZ C
Chord is 5.6 centimeters long. What is the length of ?WZ XY
0.6 centimeters
1.4 centimeters
2.1 centimeters
2.8 centimeters
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5) Jenna translated this triangle according to the rule ( 3, x – y+ 2).
Which graph shows the result?
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6) Kevin drew square WXYZ on this grid.
Kevin translated the square 3 units along the axis and -1 unit along the -axis. What are the new coordinatesx- y of the square?
W' =(-5, 3)X'= (-1,3)Y'= (-1,-1)Z' = (-5,-1)
W' =(1, 1)X' = (5, 1)Y' = (5,-3)Z' =(1, -3)
W' = (-3,5)X' = (1, 5)Y' = (1, 1)Z' = (-3,1)
W' = (-1,-1)X' = (3,-1)Y' = (3,-5)Z' = (-1,-5)
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7) Ethan transformed quadrilateral ABCD to make quadrilateral A'B'C'D'.
Are quadrilaterals ABCD and A'B'C'D' congruent? Why or why not?
No, they are not congruent. ABCD was translated to form A'B'C'D'.
Yes, they are congruent. ABCD was translated to form A'B'C'D'.
No, they are not congruent. ABCD was reflected to form A'B'C'D'.
Yes, they are congruent. ABCD was reflected to form A'B'C'D'.
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8) Ethan is proving the Exterior Angle Theorem, which states that the measure of an exterior angle of a is equal to thetriangle sum of the measures of the two remote interior angles.
Given: Triangle on line segment ABC AD
Prove: m + m = m A B BCD
StatementReason
1. on line segment ABC AD 1. given
2. m + m + m = 180°A B BCA 2. Angle Sum Theorem
3. and form a linear pairBCA BCD 3. definition of a linear pair
4. and are supplementary.BCA BCD 4. If two angles form a linear pair, then they aresupplementary.
5. ? 5. definition of supplementary angles
6. m + m + m = m + m A B BCA BCA BCD 6. substitution property of equality
7. m + m = m A B BCD 7. subtraction property of equality
What statement should Ethan Step 5 to complete the proof?add at
m = m BCA
BCD
m < m BCA
BCD
m + m BCA
= 90°BCD
m + m BCA
= 180°BCD
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9) Noah is a proof to show that opposite sides of parallelograms are congruent.writing
Given: is a parallelogram. PQRS
Prove:
Which statement should Noah step 4?add at
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10) What is the precise definition of an angle?
two rays that share a common endpoint
two line segments that share a common endpoint
the measure of an arc between two intersecting lines or line segments
one of the four intermediate spaces formed between two intersecting lines
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11) Use the graph to answer the question.
Olivia reflects the triangle over the -axis, then rotates itx 90° clockwise around the origin.
Which graph shows the resulting triangle?
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12) Rosa is proving this theorem:
Angles supplementary to the same angle congruent. are
Given: and are supplementary.
and are supplementary.
Prove:
The table shows the statements and reasons for Rosa’s proof, but they are out of order.
What is the correct order for these statements and reasons?
3, 1, 5, 4, 2
3, 5, 2, 1, 4
3, 1, 5, 2, 4
3, 5, 1, 2, 4
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13) Monica graphed the line = 3 + 2. Janice graphs a second line that is parallel to Monica’s and passes through (-2, 0). What is the equation ofy x Janice’s line?
= 3 + 6y x
= 3 – 6y x
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14) What is the equation of the line that is perpendicular to this line and passes through (-6, -2)?
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15) Ron graphed 4 different lines that all had the same slope. Which statement describes Ron’s lines?correctly
None of the lines intersect each other.
Exactly 2 lines intersect each other.
Exactly 3 lines intersect each other.
All of the lines intersect each other.
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16) Line segment is shown on the graph. AB
Emily draws point on the line so that the of AC to CB is 3 to 1. What are the coordinates of point C?C segment ratio
(-2, 2.5) (3, 0)
(-1, 2) (4, -0.5)
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17) Bob is trying to describe a sphere to his little brother. Bob decides to go through his toys to find examples of spheres. Which of the following would be a good representation of a sphere?not
a basketball
a baseball
a tennis ball
a football
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18) Mr. Jones is trying to use a geometric shape to describe a tree trunk. Which shape would best describe a tree trunk?
a cylinder
a sphere
a cube
a cone
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19) Timmie just finished a roll of paper towels. What shape is the paper towel roll?
a cone
a sphere
a cube
a cylinder
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20) Apply a dilation with a scale factor of 3 to triangle ABC. Let the image be triangle A’B’C’. Which one of the following equations is true?
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21) The coordinates for the endpoints of are L (-2, -3) and M (4, 5). is dilated by a scale factor of ( from center of dilation (3, -2) to formLM LM 1/ 2) Segment . Which statement is true?L M not
is parallel to Segment .Segment L M LM
The length of Segment is twice the length of Segment .L M LM
The length of Segment is one-half the length of .L M Segment LM
The slope of is the same as the slope of .Segment L M Segment LM
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22) The coordinates for the endpoints of are A (1, 3) and B (5, 0). is dilated by a scale factor of 3 with the origin as the centerSegment AB Segment AB
of dilation to create Segment . Which of the following will be the slope of A' B' ?A' B' Segment
Slope of cannot be determined from the information provided.Segment A' B'
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23) Use the diagram of two triangles shown below to answer this question.
Triangles ACD and ABE are similar. What is equal to?x
30.0 cm
4.8 cm
14.4 cm
10.0 cm
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24)
Triangles and are similar. ABC DEF
What is the measure of angle , rounded to the nearest tenth?C
25.8°
42.0°
64.1°
90.0°
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25) How are these two triangles related?
congruent by side-side-side
congruent by side-angle-side
congruent by angle-side-angle
similar but not congruent
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26) Triangle is similar to triangle . XYZ LMN
How long is side ?MN
2 centimeters
4 centimeters
8 centimeters
16 centimeters
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27) Which fraction represents the value of cos ? x
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28) What is the tangent of angle in this rectangle?x
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29) What is the sine of angle ?x
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30) Triangle is a right triangle.PQR
What is tan , to the nearest hundredth?Q
0.60
0.75
0.80
1.33
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31) A 60-foot flagpole was placed in front of a post office, perpendicular to the ground. After many years, the flagpole began to lean. The distance fromthe top of the flagpole to the ground is now 50 feet. Which expression shows how to determine the angle the flagpole makes with the ground?
sin A =
cos A =
sin A =
cos A =
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32) A cyclist pedals up a hill that has a 13° angle. If the cyclist pedals up the hill for 10 kilometers, what is the change in her elevation, ?x
0.22 kilometer
2.2 kilometers
9.7 kilometers
45.0 kilometers
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33) Use the diagram to answer the question.
Triangle is congruent to triangle . ABF EDF
What is the measure of angle ?FAE
28°
38°
56°
86°
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34) Use the diagram to answer the question.
The value of the tangent of angle is defined as . x
Which fact makes it possible to define the tangent of an angle?
The sum of the interior angles of a triangle equals 180°.
The angle and side measurements of congruent right triangles are equal.
All right triangles that share one congruent acute angle are similar, and therefore have equal side ratios.
For all right triangles that share one congruent acute angle, the other acute angle is also congruent.
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35) The house shown below has a symmetrical roof.
What is the measure of the angle the roof makes at the peak (angle )?x
53.1°
73.7°
102.6°
106.3°
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36) Use the triangle on the grid below to answer this question.
Triangle LMN is reflected across the Then it is reflected across the . Finally, it is translated according to the rule x -axis. y -axis ( x + 7, y + 3) . What are the final coordinates of point M'?
(4, -4)
(-3, -7)
(10, 10)
(-10,-10)
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37) Triangle is translated according to the rule .HJK
What are the coordinates of vertex after this translation?H
(-3, 3)
(-2, 1)
(1, -2)
(3, -3)
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38) Darnelle drew this figure and the accompanying equations.
+ + = 180 w x y + = 180 y z
Which equation also be true?must
+ = 180w z
– = y x w
+ + = 180w x z
+ = w x z
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I. II.
III. IV. V.
VI.
39) ABC is transformed to create A'B'C'. After the transformation, ABC A'B'C'. Which of the following transformations could have been used tocreate A'B'C' ?
( , ) ( + 3, )x y x y ( , ) (4 , 4 )x y x y ( , ) (– , )x y x y ( , ) ( , – )x y y x ( , ) (–2 , )x y x y ( , ) ( , )x y x y
I, II, V and VI only
II, III, IV, V, and VI only
III, IV, and V only
I, III, and IV only
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40) Use the diagram to answer the question.
Zhan cut a drinking straw into three pieces (shown above) to investigate a triangle postulate. He moves the straw pieces to make triangles thathave been translated, rotated, and reflected from an original position. The end of one piece is always touching the end of another piece.
Which postulate could Zhan be investigating using only these straw pieces and no other tools?
The sum of the measures of the interior angles of all triangles is 180°.
If three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent.
The sum of the squares of the lengths of the two shorter sides of a triangle is equal to the square of the length of the longest side of atriangle.
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the trianglesare congruent.
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41)Triangle is an isosceles triangle with congruent to . To prove that the baseLMN
angles and are congruent, is drawn such that point is the midpoint of asP shown in the diagram below. Complete the proof.
Given: in
is the midpoint of P
Prove:
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42) The triangle angle sum theorem states that the sum of the three interior angles of a triangle is 180 degrees. Line isd
parallel to and passes through point . An incomplete proof is provided below the diagram. C
Given: Line is parallel to d
Prove: 1 + 2 + 3 = 180 m m m
Which reason would be needed to complete this proof?
Correspondingangles theorem
Same sideinterior anglestheorem
Alternateexterior anglestheorem
Alternate interiorangles theorem
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43) Quadrilateral is a parallelogram. is a diagonal of the parallelogram. An incomplete proof is provided below the diagram.ABCD Segment BD
Given: Parallelogram ABCD
Prove: is congruent to . A C
Which statement and reason correctly complete this proof?
Statement: and
Reason: Alternate interior angles theoremStatement: and
Reason: definition of parallelogram
Statement: and
Reason: definition of parallelogram
None of the above would properly complete the proof.
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44) The diagonals of rectangle LMNP intersect at point Q.
Which method would be to use to prove that the diagonals bisect each other?best
LNM NLP by ASA
LNM NLP by SSS
LMQ NPQ by ASA
LQP NQM by SSS
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45) Determine the measure of alpha.
22 degrees
25 degrees
43 degrees
47 degrees
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46) Why does the perpendicular bisector of a segment construction work? Which theorem, postulate, or definition is used?
There is exactly one line that is going through a given point and perpendicular to a given line.
Any point on the perpindicular bisector of a segment is equidistant from the endpoints of the segment.
If a point is equidistant from the endpoints of a segment, then it's sitting on the perpendicular bisector of the segment.
Isosceles Triangle Definition
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47) Why does the construction of a parallel line through a given point work? Which theorem, postulate, definition, or construction is used?
Copy an angle construction.
There is exactly one line that is going through a given point and parallel to a given line.
If parallel lines are cut by a transversal, then the corresponding angles are congruent.
If the corresponding angles are congruent, then the lines cut by a transversal are parallel.
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48) Find the value of gamma.
37.5 degrees
52.5 degrees
30 degrees
105 degrees
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49) Use the graph to answer the question.
Which transformation carries the trapezoid itself?onto
reflect over the line = –3x
reflect over the line = –3y
reflect over the line = 3x
reflect over the line = 3y
03/25/2018 Page 51 of 51
Copyright © 2017-2018 Data Recognition Corporation.
50) Lucy draws a line on a coordinate plane.
Which transformation will result in a line perpendicular to Lucy’s line?always
reflect over the line = y x
rotate 270° clockwise around the origin
reflect over the -axis, and then reflect over the -axisx y
dilate by a factor of 2 with the origin as the center of dilation
