Honors Geometry 1. Chapter 1 Test Review Question Answers C
B
1
EC " FA = AC
3
EC ! FA = EF
F
BA " BE = ∠ABE
E
4
A
AC ! DR = A
2
∠AFD ! CE = EF
D
R
2. 43°23'16" + 25°52'45"
43°23'16"
+ 25°52'45"
68°75'61"
= 68°76'1" = 69°16'1"
90° - 28°15"
89°59'60"
- 28°00'15"
61°59'45"
3. 2
Change 27 ° to degrees, minutes, and seconds form
9
X 60
27°
120
1
' = 27°13 '
9
3
X 60
27° 13' 20"
Change 132°10" to fractional degrees
10
1
÷ 60
=
60
6
1
∴ 132° '
6
( )( )
÷ 60
∴ 132
Baroody 1
1
6
60
1
°
360
=
1
360
Page 1 of 7 Honors Geometry 4. Chapter 1 Test Review Question Answers Find the measure of the angle formed by the hands of a clock at 4:52.
12
11
1
10
Whole:
5(30°) = 150°
Minute hand: 2(6°) = 12°
8
8
Hour hand:
(30°) =
= 4°
60
2
2
9
3
∴ the ∠ measures 150 + 12 + 4 = 166°
8
4
5
7
6
5. Write the converse, inverse, and contrapositive of the following statement. Also, evaluate
whether each statement is true or false.
"If the time is 2:00, then the angle formed by the hands of a clock is acute."
If the angle formed by the hands of a clock is acute, then time is 2:00.
False
If the time is not 2:00, then angle formed by the hands of a clock is not acute.
False
If the angle formed by the hands of a clock is not acute, then time is not 2:00.
True
6. WY = 25. The ratio of WX to XY is 3:2.
Find WX.
3x
W
2x
X
3x + 2x = 25
Y
∴ WX = 3x = 3(5) = 15
5x = 25
x=5
Baroody Page 2 of 7 Honors Geometry 7. Chapter 1 Test Review Question Answers m∠ABC = 90°. Find the values of x and y.
(x + 3y) + (2x + y) = 90
A
x + 3y = 2x + y
3x + 4y = 90
2y = x
D
3(2y) + 4y = 90
(x+3y)°
(2x+y)°
B
6y + 4y = 90
C
10y = 90
y=9
x = 2(9) = 18
8. BD bisects ∠ABC and m∠ABC = 25°. Solve for x and y.
(2x - y) + (3y - x) = 25
A
(2x-y)°
B
x + 2y = 25
D
(3y-x)°
2x - y = 3y - x
3x - 4y = 0
X3
C
3x + 6y = 75
- (3x - 4y = 0)
10y = 75
y=
75
15
=
10
2
x+2
( )
15
= 15
2
x + 15 = 25
x = 10
Baroody Page 3 of 7 Honors Geometry 9. Chapter 1 Test Review Question Answers The measure of ∠A is 6 greater than twice the measure of ∠B. If the angles' sum is 42°, find the
measure of each angle.
A = 2B + 6
A + B = 42
2B + 6 + B = 42
3B = 36
m∠B = 12°
m∠A = 30°
10. Find the restrictions on AC
A
15
AC < 21 + 15 = 36
21 - 15 = 6 < AC
∴ 6 < AC < 36
C
21
11. B
∠Q is obtuse and measures (2x-28)°. Find the restrictions on x.
90 < 2x - 28 < 180
118 < 2x < 208
59 < x < 104
Baroody Page 4 of 7 Honors Geometry 12. Chapter 1 Test Review Question Answers Find a conclusion from the following statements:
Contrapositives
a
∼s
s
∼a
b
∼w
w
∼b
r
s
∼s
∼r
b
∼b
m
∼m
∼w
r
∼r
a
∼s
∼r
a
w
w
∼b
m
m
13. Construct an angle of 75° at point A that has the given ray as a side.
C
m∠CAT = 75°
A
Baroody T
Page 5 of 7 Honors Geometry 14. Chapter 1 Test Review Question Answers Construct an angle of 105° at point A which has the given ray as a side.
H
m∠HAT = 105°
A
T
15. Jennie's teacher told her to select two problems from a list of two C-level problems, five B-level
problems, and one A-level problem. If she selected at random, what is the probability that she
selected two B-level problems? What is the probability that she selected one B-level problem
and one C-level problem?
A-level 1
B-level 1
C-level 1
B-level 2
C-level 2
B-level 3
B-level 4
B-level 5
a. P(2 B-levels) = P(1st pick B-level) AND P(2nd pick B-level)
=
( )( )
5
8
4
5
=
7
14
b. P(1 B-level & 1 C-level) = P(1st pick B-level) AND P(2nd pick C-level)
OR
P(1st pick C-level) AND P(2nd pick B-level)
=
Baroody ( )( ) ( )( )
5
8
2
2
+
7
8
5
5
5
5
=
+
=
7
28
28
14
Page 6 of 7 Honors Geometry 16. Chapter 1 Test Review Question Answers If a point is chosen at random in rectangle ABCD, what is the probability that
a. It is in square SQUA?
b. It is not in square SQUA?
9
B
2
S
C
Q
3
A
D
U
ASQUA = (3)(3) = 9 u2
AABCD = (5)(9) = 45 u2
PIn the square =
9
1
=
45 5
PNot in the square =
Baroody 36
4
=
45
5
Page 7 of 7