Honors Midterm Review Name: Date: 1. Draw all lines of symmetry for these shapes. 2. Use the gure below to answer the question that follows. How many lines of symmetry does the gure have? 3. Which of the following gures appears to have both line symmetry and rotational symmetry? A. B. C. D. 4. A windmill has eight equally-spaced blades that rotate in the clockwise direction. Note: The gure is not drawn to scale. How many degrees must blade P rotate to reach the location of blade U? A. 45 B. 135 C. 225 D. 300 page 1
Transcript
Honors Midterm Review
Name: Date:
1. Draw all lines of symmetry for theseshapes.
2. Use the figure below to answer thequestion that follows.
How many lines of symmetry does thefigure have?
3. Which of the following figures appears tohave both line symmetry and rotationalsymmetry?
A. B.
C. D.
4. A windmill has eight equally-spacedblades that rotate in the clockwisedirection.
Note: The figure is not drawn to scale.
How many degrees must blade P rotateto reach the location of blade U?
A. 45◦ B. 135◦
C. 225◦ D. 300◦
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5. A fan has 5 congruent blades that arespaced equally as shown below.
What is the measure of the angle ofrotation if blade M moves clockwise tothe position of blade P?
A. 36◦ B. 45◦ C. 60◦ D. 72◦
6. The coordinates of the endpoints of−−−ST
and its image−−−−S′T ′ are given below.
S(2,−4) S′(−2,−4)
T(−1, 1) T ′(1, 1)
Which of the following singletransformations maps
−−−ST to
−−−−S′T ′?
A. translation 4 units to the left
B. rotation 180◦ clockwise about theorigin
C. reflection over the x-axis
D. reflection over the y-axis
7. The coordinates of the endpoints of−−−ST
and its image−−−−S′T ′ are given below.
S(2,−4) S′(−2,−4)
T(−1, 1) T ′(1, 1)
Which of the following singletransformations maps
−−−ST to
−−−−S′T ′?
A. translation 4 units to the left
B. rotation 180◦ clockwise about theorigin
C. reflection over the x-axis
D. reflection over the y-axis
8. The coordinates of the endpoints of−−−ST
and its image−−−−S′T ′ are given below.
S(2,−4) S′(−2,−4)
T(−1, 1) T ′(1, 1)
Which of the following singletransformations maps
−−−ST to
−−−−S′T ′?
A. translation 4 units to the left
B. rotation 180◦ clockwise about theorigin
C. reflection over the x-axis
D. reflection over the y-axis
9. The point G(2,−7) is transformedaccording to the rule (x′, y′) = (x+2, y−3).The image G′ of the transformationis then reflected over the line y = x,resulting in point G′′. What are thecoordinates of G′′?
A. (4, 10) B. (4,−10)
C. (−10, 4) D. (−4, 10)
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10. A playground is in the shape ofhexagon ABCDEF. Which of thefollowing is the best approximation ofthe amount of fencing needed to enclosethe perimeter of this playground?
A. 75 yards B. 80 yards
C. 85 yards D. 90 yards
11. Look at the triangle below.
What is the perimeter of the triangle?Round the answer to the nearest tenth ofa unit.
A. 9.3 units B. 12.0 units
C. 20.6 units D. 86.0 units
12. Triangle JKL is shown on the grid below.
What is the length of−−−KL? Round the
answer to the nearest tenth of a unit.
A. 3.2 units B. 4.0 units
C. 11.4 units D. 11.7 units
13. A triangle has vertices at (1, 3), (2,−3),and (−1,−1).
What is the approximate perimeter of thetriangle?
A. 10 B. 14 C. 15 D. 16
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14. Jill drew a circle in the coordinate plane.She then drew a diameter of the circlefrom (−3,−2) to (5, 2) as shown below.
What is the length of the diameter of thecircle that Jill drew? Round the answerto the nearest unit.
A. 4 units B. 5 units
C. 9 units D. 12 units
15. What is the distance between the points(4,−2) and (−5, 3)?
A. D =√
106 B. D =√
28
C. D =√
26 D. D =√
2
16. The point (12,−5) is units awayfrom the origin.
A. 13 units B. 25 units
C. 144 units D. 169 units
17. Points M and H are shown on thecoordinate grid below.
Point M is the midpoint of GH. Whatare the coordinates of point G?
A. (0, 1) B. (2, 1)
C. (4, 2) D. (12, 7)
18. If M(−2, 5) is the midpoint of−−−AB and
the coordinates of A are (4, 7), what arethe coordinates of B ?
A. (1, 6) B. (2, 12)
C. (8,−6) D. (−8, 3)
19. What is the midpoint of the line segmentjoining points (3, 5) and (−6, 1)?
A. (−4.5, 3) B. (−3, 6)
C. (−1.5, 3) D. (1.5, 2)
20. In parallelogram ABCD, the coordinatesof A are (4, 3) and the coordinates ofthe midpoint of diagonal
−−−AC are (2, 5).
What are the coordinates of C ?
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21. Points P(2, 9) and Q(8, 7) are on acoordinate grid. What are the coordinatesof the midpoint of
−−−PQ?
A. (3, 1) B. (5, 8)
C. (6, 2) D. (10, 16)
22. A circle has a center at (2,−3). One endpoint of a diameter is at (4,−2). Whatare the coordinates of the other endpointof that diameter?
A. (6,−1) B. (−2, 4)
C. (1,−5) D. (0,−4)
23.−−−SU intersects
−−−TV at point R. What is the
value of x, in degrees?
24. Ms. Chen drew a diagram for a newpatio in her backyard.
The measure of ∠1 is 3 times as largeas the measure of ∠2.
What is the measure of ∠2?
A. 45◦ B. 67.5◦
C. 120◦ D. 135◦
25. Use the polygon below to answer thefollowing question.
What is the total number of degrees ofthe interior angles of this polygon?
A. 64◦ B. 360◦
C. 900◦ D. 1,080◦
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26. Line ` is parallel to line m. Line t isa transversal with angle measures asindicated below.
Note: The figure is not drawn to scale.
What is the value of x?
A. 16 B. 20 C. 25 D. 32
27. In the drawing, what is the measure ofangle y?
A. 40◦ B. 60◦
C. 80◦ D. 100◦
28. Lines l and m are parallel to one anotherand cut by transversals s and t.
What is the value of x?
A. 40◦ B. 80◦
C. 120◦ D. 140◦
29. In the figure shown below,−→RS is parallel
to−−→TU, and
−−−PT intersects
−→RS at Q.
What is the measure of ∠RPQ?
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30. In the diagram below, lines h and j areparallel. Line k and line m intersectlines h and j.
Based on the angle measures in thediagram, what is m∠1?
A. 50◦ B. 60◦
C. 120◦ D. 130◦
31.
Find the measure of angle a, given thatl ‖ m, m∠EFG = 30◦ and
−−−FH ∼=
−−FI .
A. 30◦ B. 60◦
C. 90◦ D. 120◦
32. Given the diagram below, whatinformation is needed to prove that thelines are parallel?
A. m∠1 = m∠3 B. m∠1 = m∠6
C. m∠1 = m∠7 D. m∠1 = m∠8
33. In the diagram below, ∠1 ∼= ∠4.
Which of the following conclusions doesnot have to be true?
A. ∠3 and ∠4 are supplementaryangles.
B. Line l is parallel to line m.
C. ∠1 ∼= ∠3
D. ∠2 ∼= ∠3
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34. Given: angle A
What is the first step in constructing theangle bisector of angle A?
A. Draw ray−−→AD .
B. Draw a line segment connectingpoints B and C.
C. From points B and C, draw equalarcs that intersect at D.
D. From point A, draw an arc thatintersects the sides of the angle atpoints B and C.
35. A ladder is placed against a fence thatis 6 feet tall. The ladder extends 2 feetabove the fence and 3 feet behind thefence.
Note: The figure is not drawn to scale.
Which proportion can be used to find thedistance (x) between the bottom of theladder and the bottom of the fence?
A.x6
=3
8B.
x6
=2
3
C.x6
=3
2D.
x6
=8
3
36. If ^ABC ∼ ^EDF, which of thefollowing completes this proportion?
ABED
=AC?
A. EF B. DF C. BC D. ED
37. Triangle PQR is similar to triangle DEFas shown.
Which describes the relationship betweenthe corresponding sides of the twotriangles?
A.PQDE
=4
6B.
PQDE
=6
4
C.PQEF
=4
9D.
PRDE
=6
6
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38. Two similar trapezoids are shown.
Which proportion must be true?
A.MNIJ
=NKJG
B.MNIJ
=MNKL
C.MNNK
=JGIJ
D.MNIJ
=IJHI
39. A figure is shown below.
Which of the following is similar to thisfigure? (The figures are not drawn toscale.)
A.
B.
C.
D.
40. Jim is making a similar, large rectanglefrom a small rectangle as shown below.
What is the height of the large rectangle?
41. Triangle DEF is similar to triangle ABC.
What is the measure, in degrees, of ∠F?
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42. In the diagram below,quadrilateral FGHJ ∼= quadrilateral RSTV .
Based on the measurements in thediagram, what is m∠F?
A. 33◦ B. 90◦
C. 112◦ D. 125◦
43. In the diagram below, triangle ABC issimilar to triangle XYZ.
Which angle corresponds to ∠Z?
A. ∠B B. ∠C C. ∠X D. ∠Y
44. Quadrilateral FGHI is similar toquadrilateral PQRS.
Which of the following statements istrue?
A. ∠I ∼= ∠Q B. ∠G ∼= ∠S
C. ∠P ∼= ∠G D. ∠H ∼= ∠R
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45. ABCD and MNOP are similarparallelograms.
What is the perimeter of MNOP?
A. 43.2′′ B. 44′′
C. 54′′ D. 56′′
46.
In the figure above, polygons ABCDEand RSTUV are congruent. Which sidemust have the same length as side BC?
A. CD B. DE C. ST D. TU
47. Quadrilateral PQRS is shown below.
If quadrilateral WXYZ is congruent toquadrilateral PQRS, what is the measureof ∠W?
A. 45◦ B. 70◦
C. 112◦ D. 133◦
48. Trapezoid QRST is congruent to trapezoidWXYZ. Which side corresponds to TQ ?
A. XY B. YZ C. ZW D. WX
49. What is the slope of the line that isperpendicular to the line whose equationis 3x − 2y = −8?
A. 32 B. 2
3 C. −23 D. −3
2
50. Which equation represents the lineparallel to the y-axis and 4 units to theleft of the y-axis?
A. x = 4 B. x = −4
C. y = −4 D. y = 4
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51. Which is an equation of the line thatpasses through the point (2, 5) and isparallel to the x-axis?
A. x = 2 B. y = 2
C. x = 5 D. y = 5
52. Which pair of points will determine aline parallel to the y-axis?
A. (2, 3) and (−1, 3)
B. (2, 2) and (−3,−3)
C. (3, 2) and (3,−1)
D. (2,−2) and (−2, 2)
53. Which equation represents a line that isperpendicular to the line whose equationis −2y = 3x + 7?
A. y = x + 7 B. 2y = 3x − 3
C. y = 23x − 3 D. y = 3
2x − 3
54. The equation of a line is y =2
3x + 5.
What is an equation of the line that isperpendicular to the given line and thatpasses through the point (4, 2)?
A. y =2
3x −
2
3B. y =
3
2x − 4
C. y = −3
2x + 7 D. y = −
3
2x + 8
55. Find an equation of the line passingthrough the point (6, 5) and perpendicularto the line whose equation is 2y + 3x = 6.
56. What is an equation of the line thatpasses through the point (−2, 5) and isperpendicular to the line whose equationis y = 1
2x + 5?
A. y = 2x + 1 B. y = −2x + 1
C. y = 2x + 9 D. y = −2x − 9
57. Find an equation of the line passingthrough the point (5, 4) and parallel tothe line whose equation is 2x + y = 3.
58. What is an equation of the line thatpasses through the point (−2, 3) and isparallel to the line whose equation isy = 3
2x − 4?
A. y = −23x B. y = −2
3x + 53
C. y = 32x D. y = 3
2x + 6
59. The lines represented by the equationsy + 1
2x = 4 and 3x + 6y = 12 are
A. the same line
B. parallel
C. perpendicular
D. neither parallel nor perpendicular
60. Write an equation of the line that passesthrough the point (1, 6) and is parallel tothe line whose equation is y = 3x − 5.
61. Which is an equation of the line thatpasses through the point (−2, 4) and isparallel to the line y = 3?
A. x = −2 B. y = −2
C. x = 4 D. y = 4
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62. In the accompanying diagram,←→AB and
←→CD intersect at E. If m∠AEC = 2x + 40and m∠CEB = x + 20, find x.
63. The accompanying diagram showsintersecting lines ` and m. Solve for thevalue of x.
64.←→AB and
←→CD intersect at E. If
m∠AEC = 5x− 20 and m∠BED = x + 50,find, in degrees, m∠CEB.
respectively. If m∠GEB = (2x − 30) andm∠EFD = (x + 15), find the value of x.
67. In the accompanying diagram, transversal←→EF intersects parallel lines
←→AB and
←→CD at G and H, respectively. Ifm∠EGB = 2x+ 40 and m∠FHC = 3x− 10,what is the value of x?
68. As shown in the diagram below, lines mand n are cut by transversal p.
If m∠1 = 4x + 14 and m∠2 = 8x + 10,lines m and n are parallel when x equals
A. 1 B. 6 C. 13 D. 17
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69. Which diagram shows a correctmathematical construction using only acompass and a straightedge to bisect anangle?
A.
B.
C.
D.
70. A straightedge and compass were used tocreate the construction below. Arc EFwas drawn from point B, and arcs withequal radii were drawn from E and F.
Which statement is false?
A. m∠ABD = m∠DBC
B. 12 (m∠ABC) = m∠ABD
C. 2(m∠DBC) = m∠ABC
D. 2(m∠ABC) = m∠CBD
71. The diagram below shows theconstruction of line m, parallel to line `,through point P.
Which theorem was used to justify thisconstruction?
A. If two lines are cut by a transversaland the alternate interior angles arecongruent, the lines are parallel.
B. If two lines are cut by a transversaland the interior angles on the sameside are supplementary, the lines areparallel.
C. If two lines are perpendicular to thesame line, they are parallel.
D. If two lines are cut by a transversaland the corresponding angles arecongruent, they are parallel.
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72. Janet graphed a triangle on the coordinategrid shown.
Janet rotated the triangle 90◦ clockwiseabout the origin to create figure A′B′C′.What are the coordinates of the verticesof the figure A′B′C′ after the rotation?
A. A′(−4,−4)B′(−4,−2)C′(−1,−2)
B. A′(4, 4)B′(2, 4)C′(2, 1)
C. A′(−4,−4)B′(−2,−4)C′(−2,−1)
D. A′(4, 4)B′(4, 2)C′(1, 2)
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