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8.7 SimilarTriangles, Part 1Proving Similar Triangles

Standards :

GSRT.

2

GSRT.3

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# Parallel lines out with transversal

Find the missing angles.

#x.

5 i .

Given is

1=470

> 7=53

?>1--470 (given)>2:53supplementary linear Dai

>

3=530congruent tallermate' tit¥

>

4=47supplementary (linearpair 6>3 )

>

5:47 congruent (alternate to < 6)

>

6=53°

( given)

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moreold. . .

Dilatimslscalefadws

Let's consider a rectangle EFGH . pnducethelnnagefromkytttzxtzy ) .

FHH 4 -64,4)

••-••.fi#HfI.f• •

Ehl,

-42H

' ( 1,

- 2)

••T••H(2

,-4)Etkt

Recallisimilartriangkshavepnporlimab relationships.

sfiddenoothpreimnage--f¥÷=E=6±=E±Image FG

' G'H'

EH '

=E=E=ZT=E=÷=±=±z=±

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ned Similar Triangles (Part 11

Let's consider 2 triangles of different sites.

Compare the 2 triangles .

D•

**#B •

4• C #

E 8 F

Are the 2 triangles congruent ? no,

because corresponding sides are notnot equal .

Do they have the same shape ? yes ,because both are right triangles .

A ABC ~ I DE F

FE'

±¥±F¥

§=±⇒e = 's :{

. A ABC & A EFC are similar because the shape is the same &•

the

corresponding

sides have the sameratio

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slimilartrianglTwo triangles are similar if they have the Same 3 angle measurements.

° Similar triangles have same shape but possibly different sites .

tahbtnokntsimdartriangksasbeing a magnification of the other .

⇒To prove 2 triangles are similar, you must show that sides are

proportional tangles are congruent .

rearethrewaystopnve similarity :

1. Side - Side - Side (SSS) Measures of all corresponding-

sides of the Ztmangks are

g Do proportional .

theµ ¥eit¥'¥Bo H oc÷IF2.si#le5ide_ ( SAS) Measures of the 2 sides of

a.

Doo one triangle is proportionalto the corresponding 2 sides

- of the other triangle & thet.hr/XtahnegeYaYe4Ymg9IentMWe'#E F ¥?T=¥g and < Bise

.

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3.tt#e-Ang= (AH MeasureofthelanglesinA . D• onetmanglemustbe congruent

a -to the corresponding tangles

- intheothertriangle .µ#µarmB=se

€-

F

[Examples ] Determine whether the triangles are similar.Explain your

answer byeitherusingsimilarilytestorshowingwhyit 's

not similar.

ADeo Yes because$•t€.4^30 < A=cD,<B=ce .68B c ggo So

,DABC - DDEF=

because of AA .

E F

✓�2� • x h÷r=Y±Wu

7 3w/±uy%D.t ÷tE11 No

. IWVUXDXYZ because

the sides are not proportional .

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Examples ] Findlhe unknown of the following similar triangles .

�1� L 12 .

Ie:At ¥=¥a¥i¥X

J }§o 44=92422=p X = 22

Q 33

2.I%y¥ '

¥Fu Final30×-7020×=S4