Unit 7 Homefun Answers: Day #1 Unit 7 – Similarity Unit – Day 1 HF – Ratios and Proportions Simplify the following ratios – make sure the units are correct. 1. 125 5 oz lb 2. 6 1 cups pint 3. 12 4 in yd 4. 2 km 100 m Solve the following Proportions. 5. 4 16 8 a 6. 14 21 24 x 7. 3 15 60 b 8. 2 5 14 70 a 9. 3 15 12 12 x 10. 3 7 10 y y 11. 4 3 2 x x x 12. 2 3 5 4 y y y y 13. 2 3 1 7 6 x x x 14. 7 3 3 x x 15. 4 5 x x 16. 2 1 4 x x x 25 16 3 1 1 12 20 1 2 a 16 x 12 b 1 2 a 5 x 10 y 3 4 x x 1 y 9 2 x x 8 x 1 4 x x 4 3 y
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Unit 7 Homefun Answers: Day #1
Unit 7 – Similarity Unit – Day 1 HF – Ratios and Proportions
Simplify the following ratios – make sure the units are correct.
1. 125
5
oz
lb 2.
6
1
cups
pint 3.
12
4
in
yd 4.
2 km
100 m
Solve the following Proportions.
5. 4
16 8
a 6.
14
21 24
x 7.
3 15
60b 8.
2 5
14 70
a
9. 3 15
12 12
x 10.
3 7
10
y
y
11.
4
3 2
x x
x
12.
2 3 5
4
y y
y y
13. 2 3 1
7 6
x x
x
14.
73
3
x
x
15.
45x
x 16.
21
4
x
x x
25
16
3
1
1
12
20
1
2a 16x 12b
1
2a
5x 10y 3
4
x
x
1y
9
2
x
x
8x 1
4
x
x
4
3y
17. The ratio of the measures of the sides of a triangle are 2:3:4. The perimeter of the triangle is 72 feet. What is the size of the largest side? 18. The ratio of the measures of the angles of a triangle are 5:4:6; what is the size of the smallest angle? 19. A straight angle is divided into two angles whose measures are in the ratio of 2 to 7. Find the measure of the larger angle. 20. When a 5 foot vertical pole casts a 3 foot shadow, and an oak tree has a 20-foot shadow. How tall is the tree?
21. A 6 foot tall boy is standing 12 feet from a 20 foot tall lamppost. How long is his shadow, if it has a common endpoint with the shadow of the lamppost? 22. If 𝑚∠𝑃= 40°, find the ratio of the supplement of ∠𝑃 to the complement of ∠𝑃.
32
48
140
100
3
36
7
14
5
Day #2
Day #3
Day #4
YES (AA) NEI NO
15, 10 6
14, 20
17.5 ft
AA ~ NEI NEI
12 50/3
Day #4 – Proof Worksheet Day 1
Statements Reasons
𝐵𝐷̅̅ ̅̅ || 𝐶𝐸̅̅ ̅̅
Given
ABD ACE or
ADB AEC
Alt. Int. Angle
Theorem
A A Reflexive
Property
~ABD ACE AA~
Statements Reasons
𝐶𝐵̅̅ ̅̅ ∥ 𝐸𝐷̅̅ ̅̅ Given
B E or
C D
Alt. Int. Angle
Theorem
BAC DAE Vertical Angles
Theorem
~ABD ACE AA~
Statements Reasons
<P≅<S Given
Q S or
P T
Alt. Int. Angle Theorem
PRQ SRT Vertical Angles
Theorem
∆𝑃𝑅𝑄~∆𝑆𝑅𝑇 AA~
Statements Reasons
<Y and <D are right angles
Given
𝑊𝑌
𝐵𝐷=
𝑋𝑌
𝐶𝐷 Given
Y D Right Angles
Theorem
∆𝑃𝑅𝑄~∆𝑆𝑅𝑇 AA~
Statements Reasons
𝐺𝐽̅̅ ̅ ⊥ 𝐹𝐾̅̅ ̅̅ , 𝐻𝐾̅̅ ̅̅ ⊥ 𝐹𝐾̅̅ ̅̅ Given
& . FJG FKH are rt s Definition of
Perpendicular Lines
FJG FKH Right Angles
Theorem
F F Reflexive Property
∆𝑃𝑅𝑄~∆𝑆𝑅𝑇 AA~
Statements Reasons
4, 6, 5MN NQ MQ Given
6, 7.5, 9LM RM LR Given
3
2
LR LM RM
NM MN MQ Math Fact
RLM QNM SSS~
R Q CASTC
For 8 – 9, show all work on a separate sheet of paper.
8. Given: Diagram
Find: Coordinate of S so that ~QPO SRO
Statements Reasons
∠𝑍 ≅ ∠𝐺 Given
𝐻𝑍 = 10, 𝐺𝑅 = 5 Given
𝐺 𝑖𝑠 𝑡ℎ𝑒 𝑚𝑖𝑑𝑝𝑜𝑖𝑛𝑡 𝑜𝑓 𝑄𝑍̅̅ ̅̅ Given
ZG GQ Defn. Of
Midpoint
ZG GQ
Defn. of Congruent
Segments
ZQ ZG GQ Segment
Addition Postulate
ZQ ZG ZG Substitution
Prop
2ZQ ZG Math Fact
2
1
HZ ZQ
GR GQ Math Fact
~QZH QGR SAS~
7.5x
9x
CO
CW
11. Explain: Can triangles be similar and congruent at the same time?
Yes they can be. The Scale Factor would be 1:1 or 1
Day #5 – Proof Worksheet Day 2
Statements Reasons
AB=5, DE=2.5, BC=6, EF=3
Given
2 4 Given
1
2
AB BC
DE EF Math Fact
1& 2 supp.are Defn. of Supp.
3& 4 supp.are Defn. of Supp.
1 3 Supplementary Angle
Theorem
~ABC DEF SAS~
Statements Reasons
NP VR Given
NWO TWS Vertical Angles
Theorem
WNO WST or
NOW WTS
Alt. Int. Angle
Theorem
NWO SWT AA~
Statements Reasons
PIG COW Given
PG=3.2, CW=9.6, IG=4.1 Given
1
3
PG IG
CW OW CSSTP
4.1 1
3OW Substitution Prop
12.3OW Cross
Multiplication /
Math Fact
Statements Reasons
SP NR Given
RT NS Given
& . NTR NPS are rt Defn. ⊥ lines
NTR NPS Right Angle
Theorem
N N Reflexive Prop
NWO SWT AA~
Statements Reasons
AB=2, BC=8, AE=3, ED=12
Given
1
5
AB AE
BC ED Math Fact
A A Reflexive Prop
~ABC DEF SAS~
ABE ACD or
AEB ADC CASTC
BE CD Corresponding Angles
Theorem
Statements Reasons
WU=5, WX=2, UX=4,
ZU=8, YZ=15, YX=6 Given
1
3
WU UX WX
YZ XZ XY CSSTP
~WUX YZX SSS~
W Y CASTC
Statements Reasons AC=6, CD=4, BC=8, CE=3 Given
1
2
AC BC
CE CD Math Fact
ACB DCE Vertical Angles
Theorem
~ABC EDC SAS~
AB AC
ED EC CSSTP
VW
SR
SV
MJ MG NG
4.5x 6x 15x
21a 11x
~AA
4.5x
4
14
x
y
4.8
19.2
x
y
90n
4.2x
~AA~NOT
~NOT
~SAS
AG DE
EG BG
GC DC
10x 10x 20y
8
3AG
15
2FC
45
4ED
10AE
4.5x 2y 12.5x
3 4
4 3or
2
3
6
6
8
4.5
30ABCDE 22.5PQRST
3 4
4 3or
Unit 7 – Day 10 – Midsegments and Angle Bisectors in Similar Figures Solve for the following variables: 1. 2. 3.
4. 5. 6.
For 7 – 9, assume the following a Midsegments. 7. 8. 9.
26
3x
6x 21
2x
56
5x
20z 6x
57x 60x 50
DF
11EF
15.5x
8
36
x
Perimeter
20x 4m
12.75x
21.3x
Unit 7 – Day 11 – Geo Means
Find the Geometric Mean. Your answer must be radical form, NO DECIMALS!!
1. 3 and 27 2. 4 and 16 3. 7 and 28
Solve for the following variables.
4. 5. 6.
7. 8. 9.
9 8 14
100
3x
6w 5t
8w 39x 14x
10. 11. Find JL 12. Find RT
13. Find c and d 14. Find x, y, and z
Mixed Review:
15. The perimeter of the triangle shown is 33cm, find AD.