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.

Moody Mathematics

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

Property of Property of Proportions #2Proportions #2

a c b dIf thenb d a c

Moody Mathematics

Property of Property of Proportions #3Proportions #3

a c a bIf thenb d c d

Moody Mathematics

Property of Property of Proportions #4Proportions #4

a c a b c dIf thenb d b d

Moody Mathematics

Property of Property of Proportions #5Proportions #5

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

Moody Mathematics

: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

Moody Mathematics

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.

Moody Mathematics

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.

Moody Mathematics

PRACTICEPRACTICE::

Moody Mathematics

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

Moody Mathematics

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