SIMILARITY: A REVIEW A REVIEW Moody Mathematics. Midsegment: a segment that joins the midpoints of 2...

SIMILARITSIMILARITY: Y:

A A REVIEWREVIEW

Moody Mathematics

Midsegment: Midsegment: a a segment that segment that joins the joins the midpoints of 2 midpoints of 2 sides of a sides of a triangle?triangle?

Moody Mathematics

A A Midsegment Midsegment is is parallel to one parallel to one side of the side of the triangle and half triangle and half of its length. of its length.

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x

16

Find x, Find x, the length the length of the of the midsegmemidsegmentntX = X = 88 Moody

Mathematics

8

midsegmemidsegmentsnts

x

y7

20Find Find x, y, x, y, zz

z

Moody Mathematics

8

midsegmemidsegmentsnts

x

y7

20 x=8x=8, , y=1y=10, 0, z=1z=144

z

Moody Mathematics

Property of Property of Proportions #1Proportions #1

a cIf then ad bcb d

Moody Mathematics


a c b dIf thenb d a c

Moody Mathematics


a c a bIf thenb d c d

Moody Mathematics


a c a b c dIf thenb d b d

Moody Mathematics


a c a c aIf thenb d b d b

Moody Mathematics

PRACTICEPRACTICE::

Moody Mathematics

31. 3 _?_ .

5

pIf then q

q

: 5Answer pMoody Mathematics

32. _?_ .

5 5

p qIf then

q

:3

pAnswer

Moody Mathematics

3 83. _?_ .

5 5

pIf then

q

:p q

Answerq

Moody Mathematics

3 34. _?_ .

5 5

p pIf then

q q

3:5

pAnswer or

qMoody Mathematics

35. _?_ .

5

p qIf then

q p

5:3

AnswerMoody Mathematics

3 86. _?_ .

5

pIf then

q p q

5:Answerq

Moody Mathematics

DefinitionDefinition: : Polygons are Polygons are similar if: similar if: 1. 1. Corresponding Corresponding Angles are Angles are congruent 2. congruent 2. Corresponding Corresponding sides are in sides are in proportionproportion

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:ABCD RSTU means;

;

A R C T

B S D U

AB BC CD DA

andRS ST TU UR

Moody Mathematics

60

8

10

7.5

x

12

y

w

Find w, x, Find w, x, y, z in y, z in these these similar similar trapezoidtrapezoidss

z

Moody Mathematics

60

8

10

7.5

x

12

y

w

z

:

8 7.5

108

10 12

HINTS

xy

Moody Mathematics

60

8

10

7.5

x

12

y

w

W=60W=60oo

z

X=9.3X=9.37575Y=9.6Y=9.6

Z=12Z=1200oo

Moody Mathematics

Similar Similar TriangleTriangless

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AA PostulateAA Postulate: If 2 : If 2 angles of one angles of one triangle are triangle are congruent to 2 congruent to 2 angles of another angles of another triangle, then the 2 triangle, then the 2 triangles are triangles are similar.similar.

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SSS~ PostulateSSS~ Postulate: : If all 3 sides of If all 3 sides of two triangles are two triangles are in proportion, in proportion, then the triangles then the triangles are similar.are similar. Moody

Mathematics

SAS~ PostulateSAS~ Postulate: : If 2 sides of two If 2 sides of two triangles are in triangles are in proportion and proportion and their included their included angles are angles are congruent, the congruent, the triangles are triangles are similar.similar.

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PRACTICEPRACTICE::

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47

10

17.5

SimilarSimilar?? Yes by Yes by

SAS~SAS~4 7

10 17.5

(4)(17.5) (10)(7)

70 70

Moody Mathematics

Similar?Similar?66 5

8

8.4 7

11.2

Yes by Yes by SSS~SSS~5 6 8

7 8.4 11.2

(5)(8.4) (6)(7)

(6)(11.2) (8)(8.4)

Moody Mathematics

SimilarSimilar??Yes by Yes by

AAAAMoody Mathematics

62o

62o

48o

50o

SimilarSimilar?? No! No! CorrespondinCorresponding angles are g angles are not not congruentcongruent . .

68o

70o

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8

4

7

x

Find xFind x8 7

8 48 84

10.5

xx

x

Moody Mathematics

4

6

9

Find xFind x

x

6 4

96 9( 4)

6 9 36

3 36

12

x

xx x

x x

x

x

Moody

Mathematics

SIMILARITY: A REVIEW A REVIEW Moody Mathematics. Midsegment: a segment that joins the midpoints of 2...

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