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.

9x

50x

74

7y

5

15

x

d

14

14 5

7 5

x

y

z

4AD

17. Find the following variables.

18. Given 𝐻𝐹̅̅ ̅̅ ⊥ 𝐷𝐺̅̅ ̅̅ , explain why ∆𝐻𝐹𝐺~∆𝐷𝐹𝐸

19. The ratio of the measures of the 3 sides of a triangle is 3 4 5: : . Its perimeter is 48. Find the

length of the longest side.

40

3

80

7

102

x

y

z

~AA

20