Copyright © 2012 Study Island - All rights reserved.
Circles
1. A
is a segment whose endpoints are points on a circle and it passes
through the center of the circle.
A. diameter
B. radius
C. chord
D. circumference
2. If the diameter of a circle is 24 inches long, how long is the radius of the circle?
A. 96 inches
B. 48 inches
C. 6 inches
D. 12 inches
3. Which of the following line segments is a chord on circle R, shown below?
A. NQ
B. PQ
C. MR
D. RT
4. Mekhi is playing a game on a circular court. During the game, he crossed the
court by traveling from point G to point H.
Which measure corresponds to the path Mekhi traveled across the court?
A. chord
B. radius
C. circumference
D. diameter
5. Nadine is making paper cones to serve popcorn in for her birthday party. A
diagram of the paper before and after it is formed into a cone is shown below.
Nadine first cuts the circle of paper along the dashed line, and then she overlaps
the cut sides and glues them together to make a cone. If the vertex of the cone
corresponds to the center of the paper circle, which measure corresponds to the
cut Nadine makes?
A. chord
B. radius
C. circumference
D. diameter
6. A(n)
is a line segment that connects two points on a circle.
A. circumference
B. chord
C. radius
D. arc
7. The diagram below shows the cut that needs to be made to make a hole for the
sink in a bathroom countertop.
The cut is a circle where V is the center. If VW = 7 inches, what is XZ?
A. 14 in
B. 3.5 in
C. 49 in
D. 28 in
8. Vera wants to draw a chord on the circle shown below.
Where should she draw the line segment?
A. from point Y to point W
B. from point X to point Y
C. from point X to point V
D. from point Y to point Z
9. Kris wants to draw a diameter on circle L, shown below.
Where should she draw the line segment?
A. from point S to point P through point L
B. from point M to point Q through point L
C. from point L to point Q
D. from point R to point P through point L
10. Sandy is using a cutting tool to cut a circle identical to circle W, below.
If VX = 19 cm, to what length should Sandy set the radius on the tool?
A. 38 cm
B. 9.5 cm
C. 361 cm
D. 4.75 cm
Parallel, Perpendicular, & Skew Lines
1.
In the hexagonal prism above, which line is perpendicular to line MS?
A. line NO
B. line RS
C. line WR
D. line OU
2.
In the three-dimensional figure above, which line is skew to line CG?
A. line EJ
B. line CD
C. line GL
D. line HL
3.
In the three-dimensional figure above, which line is skew to line VY?
A. line WZ
B. line XZ
C. line VW
D. line UX
4.
In the pentagonal prism above, which line is perpendicular to line JK?
A. line FG
B. line FK
C. line KL
D. line EF
5.
In the three-dimensional figure above, which line is parallel to line PT?
A. line ST
B. line QR
C. none of these
D. line QT
6.
In the three-dimensional figure above, which line is parallel to line OU?
A. line QW
B. line UV
C. line OP
D. line LM
Similarity & Congruence
1. Use the trapezoid below to answer the question.
Which trapezoid is similar to trapezoid EFGH?
W.
X.
Y.
Z.
A. W
B. X
C. Y
D. Z
2. Use the triangle below to answer the question.
Which triangle is similar to triangle JKL?
W.
X.
Y.
Z.
A. W
B. X
C. Y
D. Z
3. Quadrilateral WXYZ is similar to quadrilateral QRST. Which segment corresponds
to WX?
A. ST
B. RS
C. QT
D. QR
4. Which of the triangles, labeled I, II, III, and IV, are similar to triangle XYZ?
[Note: figures not drawn to scale.]
A. I only
B. III only
C. I and II
D. III and IV
5.
Note: Figures are not drawn to scale.
In the picture above, MNJKL
VWXYZ.
If NJ = 7 inches, JK = 3 inches, KL = 9 inches, LM = 11 inches, and MN = 5
inches, what is the length of side ZV?
A. 11 inches
B. 9 inches
C. 5 inches
D. 12 inches
6.
The trapezoids above are congruent. Which side corresponds to side RS?
A. side FG
B. side EF
C. side GH
D. side HE
7.
Note: Figures are not drawn to scale.
In the picture above, JKLM
WVUT.
Which of the following sides must be congruent to side MJ?
A. WV
B. VU
C. TW
D. UT
8.
Note: Figures not drawn to scale
The pentagons above are similar. If b = 10 feet, c = 18 feet, and y = 9 feet,
what is the length of side x?
A. 18 feet
B. 5 feet
C. 10 feet
D. 2 feet
Coordinate System
1.
What are the coordinates of point S?
A. (-6, -1)
B. (6, -1)
C. (-1, -6)
D. (-1, 6)
2.
In which quadrant is point U located?
A. quadrant I
B. quadrant II
C. quadrant III
D. quadrant IV
3.
Which point is at (-9, 6)?
A. P
B. S
C. R
D. Q
4.
What are the coordinates of point K?
A. (-7, 3)
B. (7, 3)
C. (3, 7)
D. (3, -7)
5.
Which point is at (-5, 4)?
A. Q
B. R
C. S
D. P
6.
What are the coordinates of point N?
A. (-8, 5)
B. (5, -8)
C. (8, -5)
D. (-5, 8)
Answers - Circles
1. A
2. D
3. A
4. A
5. B
6. B
7. A
8. D
9. B
10. B
Explanations
1. A diameter is a chord that passes through the center of a circle.
2. The length of the radius of a circle is one-half the length of the diameter.
Divide the length of the diameter by 2 to find the length of the radius.
24 in ÷ 2 = 12 in
3. A chord is a line segment that connects two points on a circle.
Therefore, NQ is a chord on circle R.
4. Mekhi traveled between two points on the circle. So, his path is a line segment that connects two
points on a circle.
Therefore, Mekhi's path is a chord of the circle.
5. The cut Nadine makes is along a line segment whose endpoints are the center of the circle and a point
on the circle.
Therefore, the cut Nadine makes is along a radius of the circle.
6. A chord is a line segment that connects two points on a circle.
7. The diagram shows that VW is a radius of circle V and XZ is a diameter of circle V.
The length of the radius of a circle is one-half the length of the diameter.
So, XZ is twice as long as VW. Multiply VW by 2 to find XZ.
7 in × 2 = 14 in
8. A chord is a line segment that connects two points on a circle. The points on the circle shown are V, Y,
and Z.
Therefore, Vera will draw a chord if she draws a line segment from point Y to point Z.
9. A chord is a line segment that connects two points on a circle. A diameter is a chord that passes
through the center of a circle.
The center of the circle is at point L. The points on the circle are M, P, Q, and R.
So, a line segment drawn from point M to point Q is a chord of the circle.
Therefore, Kris will draw a diameter if she draws a line segment from point M to point Q through
point L.
10. The diagram shows that VX is a diameter of circle W.
The length of the radius of a circle is one-half the length of the diameter.
Divide VX by 2 to find the length of the radius.
19 cm ÷ 2 = 9.5 cm
Copyright © 2012 Study Island - All rights reserved.
Answers – Parallel, Perpendicular, Skew
1. B
2. A
3. B
4. B
5. C
6. A
Explanations
1. Perpendicular lines are lines in the same plane that intersect to form a right angle.
In the figure shown, line MS and line RS are in the same plane, and they intersect to form a right angle.
Therefore, line RS is perpendicular to line MS.
2. Two lines are skew if they do not intersect, but are also not parallel.
Since two lines in the same plane must intersect or be parallel, skew lines can exist only in three or
more dimensions.
In the figure shown, line CG and line EJ are in different planes, so they do not intersect, and they are
not parallel.
Therefore, line EJ is skew to line CG.
3. Two lines are skew if they do not intersect, but are also not parallel.
Since two lines in the same plane must intersect or be parallel, skew lines can exist only in three or
more dimensions.
In the figure shown, line VY and line XZ are in different planes, so they do not intersect, and they are
not parallel.
Therefore, line XZ is skew to line VY.
4. Perpendicular lines are lines in the same plane that intersect to form a right angle.
In the figure shown, line JK and line FK are in the same plane, and they intersect to form a right angle.
Therefore, line FK is perpendicular to line JK.
5. Parallel lines are lines in the same plane that never intersect.
Therefore, there is no line parallel to line PT in the figure.
6. Parallel lines are lines in the same plane that never intersect.
In the figure shown, line OU and line QW are in the same plane, but they never intersect.
Therefore, line QW is parallel to line OU.
Answers – Similarity and Congruence
1. D
2. A
3. D
4. A
5. A
6. A
7. C
8. B
Explanations
1. For two polygons to be similar, their corresponding sides must be proportional. The side lengths of
trapezoid Z are proportional to the side lengths of trapezoid EFGH.
Therefore, trapezoid Z, shown below, is similar to trapezoid EFGH.
2. For two polygons to be similar, their corresponding sides must be proportional. The side lengths of
triangle W are proportional to the side lengths of triangle JKL.
Therefore, triangle W, shown below, is similar to triangle JKL.
3. The statement of similarity labels the figures with their vertices in corresponding order.
Corresponding sides can be determined from the given labeling of the figures.
Therefore, the side which corresponds to WX is QR.
4. In similar triangles, corresponding side lengths are proportional.
Triangles III and IV each have two sides of equal length. In order for either of those to possibly be
similar to triangle XYZ, triangle XYZ would also have two sides of equal length.
Triangle II has side lengths which are all slightly longer than those of triangle XYZ; however, they are
not proportional.
Triangle I and triangle XYZ have corresponding side lengths which are proportional.
Therefore, triangle I is similar to triangle XYZ.
5. If two figures are congruent, corresponding sides and corresponding angles are congruent.
In this case, side ZV corresponds to side LM.
Therefore, since LM = 11 inches, ZV = 11 inches.
6. Find the side in trapezoid EFGH with identical tic marks to side RS.
Side FG corresponds to side RS.
7. If two figures are congruent, that means their corresponding sides and corresponding angles are
congruent.
In this case, side MJ corresponds to side TW.
Therefore, side MJ must be congruent to side VW.
8. Since the pentagons are similar, set up a proportion to solve for the missing side.
Therefore, side x is 5 feet long.
Answers – Coordinate System
1. B
2. D
3. A
4. B
5. D
6. A
Explanations
1. The horizontal axis is the x-axis, and the vertical axis is the y-axis.
An ordered pair is written in (x, y) format, with x being the point's
x-coordinate and y being the point's y-coordinate.
On the coordinate plane, S is 6 units to the right of the origin and
1 unit down from the origin. So, x = 6 and y = -1.
Therefore, the coordinates of point S are (6, -1).
2. The coordinate plane below shows the location of each quadrant.
Therefore, point U is located in quadrant IV.
3. The horizontal axis is the x-axis, and the vertical axis is the y-axis.
An ordered pair is written in (x, y) format, where x is the point's
x-coordinate and y is the point's y-coordinate.
To find which letter is at point (-9, 6), count 9 spaces to the left and then 6 spaces up from the origin.
Therefore, P is at point (-9, 6).
4. The horizontal axis is the x-axis, and the vertical axis is the y-axis.
An ordered pair is written in (x, y) format, where x is the point's
x-coordinate, and y is the point's y-coordinate.
On the coordinate plane, K is 7 units to the right of the origin and 3 units up from the origin. So, x = 7
and y = 3.
Therefore, the coordinates of point K are (7, 3).
5. The horizontal axis is the x-axis, and the vertical axis is the y-axis.
An ordered pair is written in (x, y) format, where x is the point's
x-coordinate, and y is the point's y-coordinate.
To find which letter is at point (-5, 4), count 5 spaces to the left and then 4 spaces up from the origin.
Therefore, P is at point (-5, 4).
6. The horizontal axis is the x-axis, and the vertical axis is the y-axis.
An ordered pair is written in (x, y) format, where x is the point's
x-coordinate, and y is the point's y-coordinate.
On the coordinate plane, N is 8 units to the left of the origin and
5 units up from the origin. So, x = -8 and y = 5.
Therefore, the coordinates of point N are (-8, 5).