Download Geometry Chapter 10

Boston Public Schools
Geometry End Chapter 10
2007-2008
Boston Public Schools
Mathematics End-Chapter Examination
Geometry
Chapter 10 (Revised 1-08)
This examination is based on the mathematics that you have done in your math class. Please do all
computation and scratch work on this examination. Choose the one best response for each multiplechoice question. Read all of the answer choices before making your selection. Please show all of your
work on the open response questions.
Diagrams on this test are not drawn to scale.
Name: ______________________________School:_____________________________
1,C,10.G.3,Geometry,Circles and Circumference,Determine Radius,Glencoe Geometry,10.1,37
Student may have:
A. found the diameter rather than the radius.
B. concluded radius and circumference were the same value.
C. used appropriate formula to solve for diameter then divided diameter by 2 to find
radius.
D. divided circumference by two but didn’t consider dividing by the value of pi.
1.
What is the radius of a given circle if the circumference of that circle is 22  ?
A. 22
B. 22 
C. 11
D. 11 
2,B,10.G.3,Geometry,Tangents and Angle Measure,Determine Exterior Angle Formed by 2 Intersecting
Tangents,Glencoe Geometry,10.6,4
Student may have:
A.
added all angle measures (360º) and divided by 2.
B.
added the measures of arcs AB and BC (286º) subtracted the measure of arc AC
(74º) and divided that difference by 2 to find the m  AZC .
C.
added the measures of arcs AB and BC (286º) divided that difference by 2 to obtain 143º
then subtracted the measure of arc AC (74º).
D.
concluded incorrectly the m  AZC was one-half the measure of arc AC (74º).
Page 1 of 7
Boston Public Schools
Geometry End Chapter 10
2007-2008
135
o
B
o
A
line m
74
o
Z
151
o
C
line p
2.
In the diagram above, if line m and line p are tangent to the circle, what is the measure of
 AZC ?
A. 180º
B. 106º
C. 69º
D. 37º
3,D,10.G.3,Geometry,Angles and Arcs,Determine Measure of a Central Angle,Glencoe
Geometry,10.2,9
Student may have:
A. concluded that 5 minutes is represented by a 30º angle. Didn’t complete problem.
B. concluded, incorrectly, that at 2 o’clock the central angle measure was 120º rather than its
supplement.
C. concluded, incorrectly, that angle formed at 2 o’clock was 90º. 90º angle is formed at 3
o’clock.
D. concluded that 2 o’clock is represented by a 60º angle.
3.
What is the measure of the angle formed by the hands of a clock at 2 o'clock?
A. 30º
B. 120º
C. 90º
Page 2 of 7
D. 60º
Boston Public Schools
Geometry End Chapter 10
2007-2008
4,A,10.G.3,Geometry,Segments in a Circle,Determine Measure,Glencoe Geometry,10.7,6
Student may have:
A. correctly used Theorem 10.15 which states: if 2 chords intersect in a circle, then the
products of the measures of the segments of the chords are equal.
B. solved for JS using an incorrect proportion.
C. failed to multiply the segment measures properly.
D. solved for JS using an incorrect proportion.
J
X
Z
S
V
4.
Using the diagram above. If VS = 14, XS = 7 and ZS = 8, what is the length of JS?
Note: Diagram is not drawn to scale.
A. 4
B. 6.5
C. 12.25
D. 16
5,A,10.G.3,Geometry,Inscribed Angles,Determine Measure, Glencoe Geometry,10.4,20
Student may have:
A. correctly concluded that the 83º angle intercepted a 166º arc, therefore the angle
of zº must intercept an arc of 194º. The angle is half its’ arc or 97º.
B. incorrectly concluded that opposite angles were of equal measure.
C. incorrectly concluded that opposite angles were complementary.
D. committed a subtraction error.
Page 3 of 7
Boston Public Schools
Geometry End Chapter 10
2007-2008
z
o
83
5.
o
In the figure above, find the value of z.
A. 97
B. 83
C. 7
D. 87
6,B,10.G.3,Geometry,Tangents,Determine Radius Measure,Glencoe Geometry,10.5,5
Student may have:
A. concluded incorrectly that answer should be under the radical sign.
B. used Pythagorean Theorem to determine ME.
C. incorrectly found the diameter measure rather than the radius.
D. added the values of MR and RE squared rather than finding the difference.
M
E
R
6.
If ER is tangent to circle M, what is the length of a radius of circle M when MR = 17 and ER =
15?
A.
8
B. 8
C. 16
Page 4 of 7
D.
514
Boston Public Schools
Geometry End Chapter 10
2007-2008
7,C,10.G.3,Geometry,Inscribed Angles,Given an Arc Find Inscribed Angle Measure,Glencoe
Geometry,10.4,7
Student may have:
A. solved for the inscribed angle incorrectly.
B. incorrectly concluded inscribed angle was twice the measure of 28º rather than half.
C. correctly concluded that an inscribed angle is ½ its inscribed arc.
D. concluded, incorrectly, the inscribed angle and its’ arc have the same measure.
7.
If the measure of arc NK = 28º, then mNCK = _____.
N
K
C
A. 32.0º
8.
B. 56.0º
C. 14.0º
D. 28.0º
In the figure below, AB = 15, BC = 17 and DE = 14. What is the length of AD?
C
B
E
D
A
A. 14
B. 15
C. 16
D. 17
8,C,10.G.3,Geometry,Secant Segments in a Circle,Find the Length of Part of a Secant Using
Proportion,Glencoe Geometry,10.7,2
Answer selected was incorrect because student:
A. did not use the secant theorem proportion correctly.
B. assumed AB and AD were congruent.
Page 5 of 7
Boston Public Schools
Geometry End Chapter 10
C.
D.
2007-2008
Correct Response
did not use the secant theorem proportion correctly.
9,A,12.G5,Geometry,Tangents,Determine the Number of Tangents Between 2 Circles,Glencoe
Geometry,10.5,30,31
9.
What is the maximum number of common tangents of the two circles shown below?
ANSWER: FOUR
10,A,10.G.3,Geometry,Secants,Determine Angle Measure of Intersecting Secants,Glencoe
Geometry,10.6,8
10.
Mass. Ave. and Columbia Road intersect as shown on the diagram below. What is the measure of
angle 1? Note: Diagram is not drawn to scale and  1 is not a central angle.
Columbia
Road
115
55
o
1
o
Mass. Ave.
85
o
Page 6 of 7
Boston Public Schools
Geometry End Chapter 10
2007-2008
ANSWER:
This item can be solved by using one of several variations of the Theorem 10.12
(pg. 561). This theorem states: If two secants intersect in the interior of a circle, then the measure of an
angle formed is one-half the sum of the measure of the arcs intercepted by the angle and its vertical
angle.
Solving Method # 1
The sum of the three given arcs (115º + 55º + 85º) is 255º. The difference between this sum and 360º
is 105º (360º - (115º + 55º + 85º)) or 360º - 255º = 105º. Using the Theorem 10.12, the
1
m1  105º + 55º  . The measure of  1 = 80º.
2
Solving Method # 2
Theorem 10.12 could also be used to find the measure of the interior angles of the 115º and 85º
1
arcs. m  115º +85º  . The measure or these vertical angles is 100º.
2
 1 is the supplement of this 100º angle. The measure of  1 = 80º.
Page 7 of 7