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HonorsGeometry
Chapter7&8ReviewQuestionAnswers
1.
If the midpoints of consecutive sides of a kite are joined in order, what is the most descriptive
name of the figure formed?
Rectangle
If the midpoints of consecutive sides of a rhombus are joined in order, what is the most
descriptive name of the figure formed?
Rectangle
If the midpoints of consecutive sides of a rectangle are joined in order, what is the
most descriptive name of the figure formed?
Rhombus
2.
The sum of the measures of the ∠s of a polygon is 5580°. Find the number of diagonals for the
polygon.
(n - 2)180 = 5580
(n - 2) = 31
n = 33
n( n - 3 )
33(30)
=
= 495 diagonals
2
2
3.
A polygon has 90 diagonals. What is its name?
n( n - 3 )
= 90
2
n(n-3) = 180
n2 - 3n - 180 = 0
(n - 15)(n + 12) = 0
n = 15 or n = -12 (which can't be since you can't have a negative number of sides)
∴ this is a pentadecagon!!
Baroody
Page1of10
HonorsGeometry
Chapter7&8ReviewQuestionAnswers
4.
The measure of an ∠ of an equiangular polygon exceeds four times the measure of one of the
polygon's exterior ∠s by 30. What is the name of the polygon?
x = interior ∠
180 - x = exterior ∠
x = 4(180 - x) + 30
x = 720 - 4x + 30
5x = 750
x = 150
Now, an exterior ∠ would measure 180 - 150 = 30°.
Since the sum of all the exterior ∠s is 360, the number of ∠s is
360
= 12.
30
A polygon with 12 ∠s is an equiangular dodecagon.
5.
What is the name of an equiangular polygon if the ratio of the measure of an interior ∠ to the
measure of an exterior ∠ is 7:2?
7x + 2x = 180 (since the exterior and interior ∠s must be supplementary)
9x = 180
x = 20°
So, an exterior ∠ is 2x or 2(20) = 40°.
Since the sum of all the exterior ∠s is 360, the number of ∠s is
A polygon with 9 ∠s is an equiangular nonagon.
Baroody
360
= 9.
40
Page2of10
HonorsGeometry
Chapter7&8ReviewQuestionAnswers
6.
7 of the ∠s of a decagon have measures whose sum is 1220°. Of the remaining 3 ∠s,
exactly 2 are complementary and exactly 2 are supplementary. Find the measure of the
smallest of these.
1440 - 1220 = 220° for the three remaining angles
x + (90 - x) + (180 - x) = 220
270 - x = 220
x = 50°
(90 - x) = 40°
(180 - x) = 130°
∴ the smallest is 40°!!
7.
The ratio of the measures of the ∠s of a heptagon is 3:4:4:4:5:5:5. Find the smallest ∠.
3x + 4x + 4x + 4x + 5x + 5x + 5x = (7 - 2)180
30x = 900
x = 30
∴ the smallest ∠ would be 3(30) = 90°
8.
If one exterior angle of a triangle is 110° and one interior angle is 80°, the measure of
the smallest angle in the triangle is what?
80°
The smallest angle measures 30°
70° 110°
30°
9.
The measures of the angles of an undecagon sum to what?
(11 - 2)180 = (9)180 = 1620°
Baroody
Page3of10
HonorsGeometry
Chapter7&8ReviewQuestionAnswers
10.
The measure of each exterior angle of a regular nonagon is what?
360
9
= 40°
11.
If
10 + x
2
y
= , find .
15 + y
3
x
3(10 + x) = 2(15 + y)
30 + 3x = 30 + 2y
3x = 2y
3=
2y
x
3
y
=
2
x
12.
Find the mean proportional (geometric mean) of the numbers 3 & 27.
3
x
=
x
27
x2 = 81
x=
81 = ±9
13.
Find the 2nd proportional for the numbers 8, 3, and 11.
3
8
=
x
11
8x = 33
x=
Baroody
33
8
Page4of10
HonorsGeometry
Chapter7&8ReviewQuestionAnswers
14.
Find x. Explain your reasoning.
Since
A
9
D
AD
AC
ACB ∼
24
x
=
3
4
and
AC
CB
=
12
16
=
3
4
DAC by SAS ∼
x
3
=
24
4
C
16
9
12
∴ we can set up the following proportion:
12
B
=
4x = 72
x = 18
15.
Find x.
4
x
=
10
15
4
2
x
=
5
15
10
x
5x = 30
x=6
15
16.
The perimeter of
ABC = 25. Find BC.
15 - x
x
=
4
6
B
4x = 90 - 6x
x
15 - x
10x = 90
x = 9 = BC
A
Baroody
4
D
6
C
Page5of10
HonorsGeometry
Chapter7&8ReviewQuestionAnswers
17.
Find AB & BE.
6
BE
A
6
D
9
6
B
12
E
=
9
9
12
15
=
6
AB
6
3
=
BE
4
3
6
=
5
AB
3(BE) = 24
3(AB) = 30
BE = 8
AB = 10
C
18.
Find NR + NS.
N
5x - 21
5x - 21
5
=
x
8
x
5x = 40x - 168
8
5
35x = 168
R
S
x=
∴ NR = 5
168
24
=
35
5
( )
24
- 21 + 5
5
= 24 - 21 + 5 = 8
NS =
=
Baroody
24
+8
5
24
40
64
+
=
5
5
5
NR + NS = 8 +
64
40
64
104
=
+
=
5
5
5
5
Page6of10
HonorsGeometry
Chapter7&8ReviewQuestionAnswers
19.
Find P
x-2
HFJ
4
F
9
H
4
(x - 6)(x + 7) = 0
x = 6 and/or x = -7
x+3
J
y
(x - 2)(x + 3) = 36
x2 + x - 42 = 0
K
5
x+3
x2 + x - 6 = 36
x-2
G
9
=
since FG can't be < 0
∴ FG = 6 - 2 = 4 & KJ = 6 + 3 = 9
4
5
=
13
y
So, P
=9+4+4+9+
= 26 +
4y = 65
y=
HFJ
65
4
=
65
4
65
4
104
65
169
+
=
4
4
4
20.
Find all possible values for y.
y
12
=
27
y
12
y2 = 324
y
y
y = ±18
However, since y can't be < 0, the
only viable answer is y = 18.
27
Baroody
Page7of10
HonorsGeometry
Chapter7&8ReviewQuestionAnswers
21.
Find y.
Using Theorem 66, we can see that
12
y
6
18
12
8
=
18
12
12
3
=
y
2
12
y
3y = 24
4
y=8
22.
Given:
C
ABDF is a !
B
A
D
Prove:
CBD ∼
DFE
F
E
Statements
1. ABDF is a !
2. AC
DF; BD
1. Given
2. Opposite Sides of a ! are
AE
A 3. ∠C ≅ ∠EDF
A 4. ∠CDB ≅ ∠E
5. CBD ∼ DFE
Baroody
Reasons
3. PCA
4. PCA
5. AA∼ (3, 4)
Page8of10
HonorsGeometry
Chapter7&8ReviewQuestionAnswers
23.
DH
HF
Given:
CD
Prove:
DE
C
CB
BG
=
D
H
B
GF
FE
F
G
Statements
1. DH
2.
3.
4.
CD
DE
GF
FE
CD
DE
CB; HF
=
=
=
E
BG
Reasons
1. Given
BH
2. Side-Splitter Theorem
HE
BH
3. S. A. 2
HE
GF
4. Subsititution (3 into 2)
FE
24.
J
Given:
HR
GM
Prove:
PR
PH
=
OM
OG
R
M
P
Reasons
GM
1.
2.
3.
4.
A 2. ∠JRP ≅ ∠M
A 3. ∠JPR ≅ ∠JOM
4. JPR ∼ JOM
PR
JP
5.
=
OM
JO
Baroody
Given
PCA
PCA
AA ∼ (2, 3)
5. CSSTP
A 6. ∠JPH ≅ ∠JOG
A 7. ∠JHP ≅ ∠G
8. JPH ∼ JOG
PH
JP
9.
=
OG
JO
10.
G
O
Statements
1. HR
H
6. PCA
7. PCA
8. AA ∼ (6, 7)
9. CSSTP
PR
PH
=
OM
OG
10. Substitution (9 into 5)
Page9of10
HonorsGeometry
Chapter7&8ReviewQuestionAnswers
25.
Given:
Prove:
YSTW is a parallelogram
SX ⊥ YW
SV ⊥ WT
Y
X
W
V
SX · YW = SV · WT
T
S
Statements
1. YSTW is a !
A 2. ∠Y ≅ ∠T
3. SX ⊥ YW
4. ∠SXY is a right ∠
5. SV ⊥ WT
6. ∠SVT is a right ∠
A 7. ∠SXY ≅ ∠SVT
8. SXY ∼ SVT
SX
SY
9.
=
SV
ST
10. SX · ST = SV · SY
11. ST ≅ YW; SY ≅ WT
12. ST = YW; SY = WT
13. SX · YW = SV · WT
Baroody
Reasons
1. Given
2. Opp. ∠s of ! are ≅
3. Given
4. Defn. of ⊥
5.
6.
7.
8.
Given
Defn. of ⊥
RAT
AA ∼ (2, 7)
9. CSSTP
10. Means-Extremes Products Thm.
11. Opp. sides of parallelogram are ≅
12. Definition of ≅ Segments
13. Substitution (12 in 10)
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