Chapter(1(–(Basics(of(Geometry( Answer'Key(
CK512(Basic(Geometry(Concepts( 1(
1.1 Basic Geometric Definitions
Answers
Possible Answers for 1-4. Answers may vary.
1. 2.
!
3. 4.
5. This problem describes any quadrilateral with the diagonals drawn in.
6. 𝑊𝑋
, 𝑋𝑊, 𝑊𝑌, 𝑌𝑊, 𝑋𝑌, 𝑌𝑋 and line m.
!
7. 𝑇𝑅
, 𝑇𝑆, 𝑅𝑇, and 𝑆𝑇.
8. Plane V, Plane RST, Plane RTS, Plane STR, Plane SRT, Plane TSR, and Plane TRS.
A
C
B
D
E
W
Y
Z
X
G
H
P
Q
Chapter(1(–(Basics(of(Geometry( Answer'Key(
CK512(Basic(Geometry(Concepts( 2(
9. A soccer field is like a plane since it is a flat two-dimensional surface. Student could
also say it is a rectangle.
10. Possible Answers sun rays, laser beam, the hands on a clock, foul lines on a baseball
field, the light from a flashlight.
11. A line and a plane intersect at a point.
12. A postulate is assumed true and a theorem must be proven true. All postulates, by
definition, are true. You must be told (or shown in a proof) that a theorem is true before
you can use it in a proof or otherwise.
13. Possible Answer 𝑃𝑄
intersects 𝑅𝑆 at point Q.
14. Possible Answer 𝐴𝐶
and 𝐴𝐵 are coplanar but point D is not.
15. Possible Answers Points E and H lie in Plane J, but 𝐸𝐹
and 𝐻𝐺 do not. Points E and
H are coplanar, but 𝐸𝐹
and 𝐻𝐺 are non-coplanar.
16. Possible Answer 𝐼𝑀
, 𝐼𝐿 , 𝐼𝐾, and 𝐼𝐽 have I as the endpoint, but J, K, L and M are non-
collinear.
17. True.
Chapter(1(–(Basics(of(Geometry( Answer'Key(
CK512(Basic(Geometry(Concepts( 3(
18. False. To make this a true statement, it should say three non-collinear points determine
a plane. If three points are collinear, then they can be in infinitely many planes.
19. False. See the picture.
20. False. To make this a true statement, it should say a line segment is the set of infinitely
many collinear points between two endpoints.
21. False, by definition a point is “zero dimensional” and does not take up space.
22. True.
23. False. See the picture.
24. False, the endpoint, A, must be first.
25. True.
Chapter(1(–(Basics(of(Geometry( Answer'Key(
CK512(Basic(Geometry(Concepts( 4(
1.2 Distance Between Two Points
Answers
For questions 1-8, your answers may vary, depending on the size of paper you printed
these questions on. These answers are for 100% on a 8.5” x 11” piece of paper.
1. 2.75 in
2. 4.9 cm
3. 4.125 in
4. 8.2 cm
5.
B
A
T
6. O is the midpoint. LO = OT = 8 cm.
7. a)
T
A
Q
b) TA + AQ = TQ
c) TQ = 15 in
8. a)
b) HM + MA = HA
c) MA = 11 cm
9. a)
M
I
T
b) MI + IT = MT
c) MI = 19 cm
10.
A
B
D
C
!
BC = 8 cm, BD = 25 cm, CD = 17 cm
Chapter(1(–(Basics(of(Geometry( Answer'Key(
CK512(Basic(Geometry(Concepts( 5(
11.
F
H
G
E
!
FE = 8 in, 13 in = HG, FG = 17 in
12. x = 3, HJ = 21 units, JK = 12
13. x = 11, HJ = 52 units, JK = 79 units
14. 13 units
15. 5 units
16. 9 units
17. 5 units
18.
19. SV = 6 units, TS = 23 units, RS = 17 units, TV = 29 units
20. x = 3
Chapter(1(–(Basics(of(Geometry( Answer'Key(
CK512(Basic(Geometry(Concepts( 6(
1.3 Congruent Angles and Angle Bisectors
Answers
1.
PS
2.
90°
3.
45°
4.
45°
5.
20x =°
6.
14x =°
7. True
8. False
9. False; it divides an angle into two congruent angles.
10. True
Chapter(1(–(Basics(of(Geometry( Answer'Key(
CK512(Basic(Geometry(Concepts( 7(
1.4 Midpoints and Segment Bisectors
Answers
1. (students may not have angle markings)
2. 𝑉𝑆
and 𝑄𝑇
3. 𝑉𝑆
bisects 𝑄𝑇
4. 𝑄𝑇
bisects 𝑉𝑆 You could also say that the lines bisect each other from what we know in
#3.
5.
12x =
6. (3, −5)
7. (1.5, −6)
8. (5, 5)
9. (−4.5, 2)
10. (−0.5, −2)
11. B is (7, 10)
12. A is (6, 9)
A
D
B
C
Chapter(1(–(Basics(of(Geometry( Answer'Key(
CK512(Basic(Geometry(Concepts( 8(
1.5 Angle Measurement
Answers
1.
32mLMN∠=°
2.
15x =°
3. False, B is the vertex.
4. True
5. True
6. False, it is equal to the sum of the smaller angles within it.
7. 8.
9. 10.
! ! ! !
!
Chapter(1(–(Basics(of(Geometry( Answer'Key(
CK512(Basic(Geometry(Concepts( 9(
11. 12.
For questions 13-16, student answers might be off by 1° or 2° .
13. 40°
14. 122°
15. 18°
16. 87°
17.
10x =°
Chapter(1(–(Basics(of(Geometry( Answer'Key(
CK512(Basic(Geometry(Concepts( 10(
1.6 Angle Classification
Answers
1. False, two angles could be 5° and 30°.
2. False, it is a straight angle.
3. True
4. True
5. Acute
6. Obtuse
7. Obtuse
8. Acute
9. Obtuse
10. Acute
11. Possible Answer
12.
100mQOP∠=°
13.
130mQOT∠=°
14.
30mROQ∠=°
15.
70m SOP∠=°
O
R
S
Q
P
T
160°
100°
Chapter(1(–(Basics(of(Geometry( Answer'Key(
CK512(Basic(Geometry(Concepts( 11(
1.7 Complementary Angles
Answers
1. 86
°
2. 1
°
!
3. 36
°
4. 58
°
5. 63
°
6.
90 ( )xy°− + °
7.
90 z°− °
or
( )
90 z−°
8.
INJ∠
and
KNJ∠
9.
27mKNJ∠=°
10. False, they add up to 90
°
11. False, they can be the sum of any two angles where their sum is 90
°
.
Chapter(1(–(Basics(of(Geometry( Answer'Key(
CK512(Basic(Geometry(Concepts( 12(
1.8 Supplementary Angles
Answers
1. 66
°
2. 169
°
3. 89
°
4. 96
°
5. 123
°
6.
180 x°− °
or
( )
180 x−°
7.
180 ( )xy°− + °
8. Possible Answer
JNI∠
and
INM∠
9. 117
°
10. True
11.
17x =°
12.
10.5x =°
Chapter(1(–(Basics(of(Geometry( Answer'Key(
CK512(Basic(Geometry(Concepts( 13(
1.9 Linear Pairs
Answers
1. False, they are supplementary.
2. True
3. False, they are next to each other.
4. True
5. False, they can form linear pairs, but not all the time.
6.
34x =°
7. 119
°
8. 147
°
9. 66
°
10. 173
°
11. 1
°
12.
180 z°− °
or
( )
180 z−°
Chapter(1(–(Basics(of(Geometry( Answer'Key(
CK512(Basic(Geometry(Concepts( 14(
1.10 Vertical Angles
Answers
1. Possible Answer
INJ∠
and
MNL∠
2.
63mMNL∠=°
3. True
4. 64
°
5. 42
°
6. 27
°
7. 21
°
8. 32
°
9. 4
°
10. 21
°
! !
Chapter(1(–(Basics(of(Geometry( Answer'Key(
CK512(Basic(Geometry(Concepts( 15(
1.11 Triangle Classification
Answers
1. Acute scalene
2. Equiangular equilateral
3. Right isosceles
4. Obtuse scalene
5. Acute isosceles
6. Obtuse isosceles
7. No, because a right angle is 90
°
and an obtuse angle is greater than 90
°
. That would
be a sum greater than 180
°
and a triangle’s three angles must add up to exactly 180
°
.
8. No, same reasoning as #7. Two obtuse angles would add up to be greater than 180
°
.
9. True.
10. False, triangles are named after the largest angle.
Chapter(1(–(Basics(of(Geometry( Answer'Key(
CK512(Basic(Geometry(Concepts( 16(
1.12 Polygon Classification
Answers
1. Concave pentagon
2. Convex octagon
3. Convex 17-gon
4. Convex decagon
5. Concave quadrilateral
6. Concave hexagon.
7. A is not a polygon because two of the sides do not meet at a vertex; B is not a polygon
because one side is curved; C is not a polygon because it is not closed.
8. 2 diagonals 9. 5 diagonals 10. 9 diagonals
11. Nonagon: 21, Decagon: 35, Undecagon: 44, Dodecagon: 54
12. True
13. False, a star is a concave polygon.
14. True, see the picture.
!
!
!