Solution Manual for Geometry, 1st Edition

Name: Solution Manual for Geometry, 1st Edition
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Solution Manual for Geometry, 1st Edition is packed with detailed solutions to help you grasp concepts effortlessly.

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INSTRUCTOR’S
S OLUTIONS MANUAL
GEX P UBLISHING S ERVICES
G EOMETRY
Elayn Martin-Gay
University of New Orleans

Table of Contents
Chapter 1 A Beginning of Geometry ................................................................................. 1
Chapter 2 Introduction to Reasoning and Proofs ............................................................. 30
Chapter 3 Parallel and Perpendicular Lines ..................................................................... 56
Chapter 4 Triangles and Congruence ............................................................................... 91
Chapter 5 Special Properties of Triangles...................................................................... 120
Chapter 6 Quadrilaterals................................................................................................. 156
Chapter 7 Similarity ....................................................................................................... 185
Chapter 8 Transformations............................................................................................. 216
Chapter 9 Right Triangles and Trigonometry ................................................................ 247
Chapter 10 Area ............................................................................................................. 290
Chapter 11 Surface Area and Volume............................................................................ 346
Chapter 12 Circles and Other Conic Sections................................................................ 404

1
Chapter 1
Section 1.2 Practice
1. Each figure is a square divided into four
smaller squares, with one of the smaller
squares shaded with an X in it. So, predict
that the next figure is a square divided into
four smaller squares, with the upper-right
square shaded and marked, as sketched
below.
2. a. The second number is the first plus 2, the
third is the second minus 3, the fourth is
the third plus 4, and the fifth is the fourth
minus 5. So, predict that the sixth is the
fifth plus 6, or 3.
b. Each number is 1
3 of the previous
number, so predict that the next number is
1 .
81
3. No. None of the angles are marked, so we
may not conclude that they have the same
measure.
Vocabulary & Readiness Check 1.2
1. defined term
2. undefined term
3. A statement that we prove is called a
theorem.
4. A statement that we accept as true but do not
prove is called an axiom or a postulate.
Exercise Set 1.2
2. Each figure is a light brown rectangle divided
into 1 more equal-sized section than the
previous figure. A sketch of the next figure is
provided.
4. Each figure is a square divided into 4
different colored squares. Each figure is the
previous image rotated 90° clockwise. A
sketch of the next figure is provided. G
stands for green, R stands for red, B stands
for blue, and Y stands for yellow.
6. Each subsequent figure has 1 square added
on top of the existing columns, and 1 square
added to the right. The next figure should
have 4 squares in the first column, 3 in the
second column, 2 in the third column, and 1
in the fourth column. A sketch of the next
figure is provided.
8. The figures are rectangles that alternate
between tan and green. There is an X in a
bottom corner of each tan rectangle, and in a
top corner of each green rectangle. The X
switches from left to right in figures with the
same color. The next figure will be green
with an X in the top right corner. A sketch of
the next figure is provided.
10. The figures are green right triangles. The
second figure is the first figure reflected
vertically. The third figure is the second
figure reflected horizontally. The next figure
will be the third figure reflected vertically. A
sketch of the next figure is provided.
12. Each number is 2 more than the previous
number, so predict that the next two numbers
are 2 and 4.

Chapter 1: A Beginning of Geometry ISM: Geometry
2
14. Each number has a denominator that is one
larger than the denominator of the previous
number when written as a fraction, so predict
that the next two numbers are 1
5 and 1 .
6
16. Each number is 3 times the previous number,
so predict that the next two numbers are 162
and 486.
18. Each number is half of the previous number,
so predict that the next two numbers are 1
40
and 1 .
80
20. Add 1 to the first number to get the second
number, and add 1 to the second number to
get the third number. Subtract 1 from the
third number to get the fourth number, and
subtract 1 from the fourth number to get the
fifth number. So, a pattern could indicate to
add 1 to the fifth number to get the sixth
number, and add 1 to the sixth number to get
the second number. So, predict that the next
two numbers are 0 and 1.
22. Yes. The figure has 3 sides that are
connected, which is the requirement for being
called a triangle.
24. No. The figure is a triangle because it has 3
connected sides, but no indication is provided
that one of the angles is a right angle.
26. Yes. Both angles measure 37°, so they have
the same measure.
28. No. No indication is provided that the
segments are the same length.
30. Yes. Both angles have the middle ray as a
side.
32. No. The opposite sides of the figure are not
marked parallel, so it cannot be concluded
that the figure is a parallelogram.
34. The student’s number is not correct. Since
the number that follows 1
4 is 1 ,
6 the
denominator is not doubled to get the next
denominator. Add 2 to the denominator to get
the next denominator. Therefore, the next
number in the list is 1 .
8
36. The student’s figure is not correct. In this
pattern, the positions of the dot and the x are
reversed to generate the next figure. Then the
image is flipped vertically to generate the
next figure. The correct figure should have
the positions of the dot and the x reversed, as
shown.
38. Neither axioms nor postulates are proven.
They are accepted as true.
Section 1.3 Practice
1. a. Two other ways to name EH
HJJG are HE
HJJG
and line .n
b. There are many correct answers. Two
other ways to name plane M are plane
GED and plane .GFD
c. Points ,D ,E and F lie on the same
line, so they are collinear.
d. Points ,D ,E ,F and G lie on the same
plane, so they are coplanar.
e.

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Chapter 1: A Beginning of Geometry ISM: Geometry
4
24. There are many correct answers. Sample
Answer: Points ,A ,E and B are not
collinear.
26. There are many correct answers. Sample
Answer: Points ,W ,A and X are not
collinear.
28. False. Point D lies on line ,l not line .m
30. True. Point C does lie on line .m
32. True. Points ,D ,E and B are collinear
because they all lie on the same line, line .l
34. False. The fact that the points are collinear
means that many planes pass through these
three points, not just one.
36. The plane intersects in

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