Quarter 1 Review Answers
1.1
1.
Sample answer:
2.
5. EF
4. L or F
6. M
7. A, D, G, F, or L
8. E
3.
9. EG & EF or EC & ED
10. C, E 11. E
12. C or D
13. infinite; zero
_______________________________________________________________________________________________
1.2
1. 18
2. 12
3. 12.1
5. 2 x  25  x  32; x  7; AB  27; BC  12; AC  39
4. about 1020 mi
6. 13x  4  74; x  6; AB  53; BC  21; AC  74
7. 51.8 mi; the third day
____________________________________________________________________
1.3
1. MW ; 38
2. line ; 30
8. 5
9. 5
3.
2, 7
4.
0, 3
6. 5, 13
5. 3, 0
s2  s2 
10. no; If one side of the square is s, then the length of the diagonal is
10  3.2
7.
2s2  s 2.
11. about 4 mi; about 10.5 mi
______________________________________________________________________
1.4
1. quadrilateral; convex
2. hexagon; concave
3. about 16.5 units
4. A = 21 square units
P = 6  2 58  21.23units
5. A = 28 square units P = 22 units
_______________________________________________________________________________
1.5 Practice A
1. 50; acute
8.
23
9.
2. 90; right
BEH , CFI
3. 130; obtuse
10.
EBH ,
4. 180; straight
FCI ,
DGA,
EHB,
5. 44
FIC
6.
46
11. 92˚
7.
47
12. 44˚
_______________________________________________________________________
1.6
1. FJG, GJH
2. CAD, EJF
3. BAC , EJG
7. yes; The sides form two pairs of opposite rays.
9. x   x  24  180; 78 and 102


11. x  12 x  15  180; 50 and 130
4.
54
5.
105
6. 4 and 5
8. no; The sides do not form two pairs of opposite rays.
10. x  3x  90; 22.5 and 67.5
2.1
1. If you like the ocean, then you are a good swimmer.
3. a.
b.
c.
d.
2.
If it is raining outside, then it is cold.
conditional: If an animal is a puppy, then it is a dog; true
If an animal is a dog, then it is a puppy; false
If an animal is not a puppy, then it is not a dog; false
If an animal is not a dog, then it is not a puppy; true
4. An angle is obtuse if and only if the angle measure is greater than 90 and less than 180.
5. Two angles are supplementary if and only if the sum of their angle measures is 180.
6. A true biconditional statement can be written when the conditional statement and its converse are both true.
_______________________________________________________________________
2.2
1. inductive reasoning; The conjecture is based on the assumption that the weather pattern will continue.
2. deductive reasoning; The conjecture is based on the fact that 92  14  1288, which is even.
3. inductive reasoning; The conjecture is based on the assumption that a pattern will continue.
4. deductive reasoning; The facts of mammals and laws of logic were used to draw the conclusion.
5. Sample Answer:
150˚
The angles are vertical but are not complementary since their
sum is not 90˚.
150˚
6. Sample Answer:
70˚
110˚
The angles are supplementary, but are not a
linear pair.
7. Sample Answer: 99˚. (The angle is obtuse, but its measure is < 100˚.)
_______________________________________________________________________
2.3
1. Line Point Postulate
2. Line Intersection Postulate
3. Plane Point Postulate
4. Plane Line Postulate
5. Two Point Postulate
6. Three Point Postulate
7. Yes
8. Yes
12. No (they intersect at XY .)
9. Yes
10. No (it’s in plane K)
13. Yes
14. Yes
11. Yes
15. No, (it’s in plane V)
16. Yes; It would look like the pages of a book where the pages are the plane and the spine of the book is the line
where they intersect.
_______________________________________________________________________
A2
Geometry
Answers
Copyright © Big Ideas Learning, LLC
All rights reserved.
2.5
2.4
1. Equation
Explanation and Reason
3 x  4  31
Write the equation; Given
3 x  27
Divide each side by 3;
Division Property of Equality
2. Equation
16 x
3.
Subtract 4 from each side;
Subtraction Property of Equality
x  9
1
2
1.Symmetric Property of Segment Congruence
2.Reflexive Property of Angle Congruence
Explanation and Reason
 18  2 x  16 Write the equation;
Given
8 x  4  2 x  32
Multiply; Distributive
Property
6 x  36
Add 4 to each side
and subtract 2 x from
each side; Addition
and Subtraction
Properties of Equality
x  6
3.
Divide each side by 6;
Division Property of
Equality
Equation
2
1. FB bisects AFC
1. Given
2. AFB  BFC
2. Definition of
angle bisector
3. CFD  BFC
3. Given
4. BFC  CFD
4. Symmetric Property
of Angle Congruence
5. AFB  CFD
5. Transitive Property
of Angle Congruence
2.6 Practice A
2.6 Practice A
Subtract  r 2 from
each side; Subtraction
Property of Equality
S  r2
 s
r
Divide each side by  r;
Division Property of
Equality
2
2.
STATEMENTS
REASONS
1. 1 and 2 are
supplementary.
1. Given
1 and 3 are
supplementary.
2. m1  m2  180
m1  m3  180
3. m1  m2
5. Transitive Property of Equality
6. Multiplication and Subtraction Properties of
4. m2  m3
4. Subtract. Prop.
of Equality
5. 2  3
5. Definition of
congruent angles
3.
is
a right
angle.
Given
Equality
8.
9. GH
3x; 21
10.
11.
60
12.
Vertical Angles
Congruence
Theorem
(Thm. 2.6)
30  mK
7. Symmetric Property
3x  y  5 x  2 y
13. 57.5˚
is
a right
angle.
Given
is
a right
angle.
Right Angle
Congruence
Theorem
(Thm. 2.3)
Right Angle
Congruence
Theorem
(Thm. 2.3)
Definition of a
right angle
are
supplementary.
angle
Given
Copyright © Big Ideas Learning, LLC
All rights reserved.
2. Definition of
supplementary
angles
3. Transitive
Property
 m1  m3
Rewrite the equation;
Symmetric Property
of Equality
4. Multiplication Property of Equality
2. x  7, y  7
1. x  5, y  19
Write the equation;
Given
S   r 2   rs
S  r
r
REASONS
Explanation and Reason
S   rs   r
s 
STATEMENT
Subtraction
Property of
Equality
is
a right
angle.
Definition
of a right
angle
Definition of
supplementary
angles
Geometry
Answers
A3
3.1 Practice A
1. AB and CD
2. AC and CD
3. no; AB CD and by the Parallel Postulate (Post. 3.1), there is exactly one line parallel to AB through point C.
4. no; They are intersecting lines.
5. 2 and 8, 3 and 5
7. 1 and 5, 2 and 6, 3 and 7, 4 and 8
9. alternate interior
13. consecutive exterior
10. corresponding
6. 1 and 7, 4 and 6
8. 2 and 5, 3 and 8
11. alternate exterior
14.
12. corresponding
No; the lines will not always be skew.
There could be another plane that contains
both lines. Then, the lines would be parallel.
3.2
1. m1  41, m2  41; m2  41 by the Corresponding Angles Theorem (Thm. 3.1). m2  41 by the
Vertical Angles Congruence Theorem (Thm. 2.6).
2. m1  124, m2  124; m2  124 by the Alternate Exterior Angles Theorem (Thm. 3.3). m2  124 by
the Vertical Angles Congruence Theorem (Thm. 2.6).
3. 16;  x  24   3 x  8 
x  32  3 x
32  2 x
16  x
4.
51;
2
 x  27  3x  25
3
2
x  18  3 x  25
3
11
x 7
3
x
 180
 180
 180
 51
5. m1  102, m2  102, m3  78; Because the given 102 angle is an alternate interior angle with 1, they
are congruent by the Alternate Interior Angles Congruence Theorem (Thm. 3.2). Because the given 102 angle and
2 are alternate exterior angles, they are congruent by the Alternate Exterior Angles Theorem (Thm. 3.3).
Because 2 and 3 are a linear pair, they are supplementary by the Linear Pair Postulate (Post. 2.8).
6. m1  68, m2  68, m3  112; Because the given 68 angle and 1 are corresponding angles, they are
congruent by the Corresponding Angles Theorem (Thm. 3.1). Because 1 and 2 are alternate exterior angles,
they are congruent by the Alternate Exterior Angles Theorem (Thm. 3.3). Because angle 2 and 3 are
consecutive angles, they are supplementary by the Consecutive Interior Angles Theorem (Thm. 3.4).
7. m1  110, m2  70; Because 3x  5   4x  30 , the value of x is 35. So, 3x  5   110 and
4x  30
 110. By the Corresponding Angles Theorem (Thm. 3.1), m1  110. By the Linear Pair
Postulate (Post 2.8), m2  70.
8. 3, 5, 6, 7, 9, and 10; Because 1 and 3 are supplementary to 2 by the Consecutive Interior Angles
Theorem (Thm. 3.4), 1  3 by the Congruent Supplements Theorem (Thm. 2.4). 1  5 and 1  7 by
the Alternate Interior Angles Theorem (Thm. 3.3). 1  6 by the Vertical Angles Congruence Theorem (Thm.
2.6). Because 3  9 by the Vertical Angles Congruence Theorem (Thm. 2.6), 1  9 by the Transitive
Property of Angles Congruence. Because 5  10 by the Vertical Angles Congruence Theorem (Thm. 2.6),
1  10 by the Transitive Property of Angles Congruence (Thm. 2.2).
A4
Geometry
Answers
Copyright © Big Ideas Learning, LLC
All rights reserved.
3.3
1. x  12; Lines s and t are parallel when the
2. x  26; Lines s and t are parallel when the marked
marked alternate exterior angles are congruent.
4 x  16  7 x  20
consecutive interior angles are supplementary.
2 x  15  3 x  20  180
36  3x
2 x  30  3 x  20  180
12  x
5 x  50  180
5 x  130
x  26
3.yes; Alternate Exterior Angles Converse (Thm. 3.7)
4. yes; Consecutive Interior Angles Converse
(Thm. 3.8)
5.yes; Corresponding Angles Converse (Thm. 3.5)
6. no; There is not enough information.
7.
8.
STATEMENTS
REASONS
1. 1  2
1. Given
2. c
2. Alternate Exterior
Angles Converse
(Thm. 3.7)
d
3. 2  3
3. Given
4. a
4. Alternate Interior
Angles Converse
(Thm. 3.6)
b
5. 3  4
5. Corresponding Angles
Theorem (Thm. 3.1)
6. 1  4
6. Transitive Property
of Angle Congruence
(Thm. 2.2)
Copyright © Big Ideas Learning, LLC
All rights reserved.
STATEMENTS
REASONS
1. 1 and 2 are
supplementary.
1. Given
2. 2 and 3 are
supplementary.
2. Linear Pair Postulate
(Post 2.8)
3. 1  3
3. Congruent
Supplements
Theorem
(Thm. 2.4)
4.
p
q
4. Corresponding
Angles Converse
(Thm. 3.5)
Geometry
Answers
A5