Proving Triangles Similar through SSS and SAS

CH 6.5

Side Side Side Similarity Theorem

• If the corresponding side lengths of 2 triangles are proportional, then the triangles are similar

To prove 2 triangles similar using SSS

• In order to prove similarity using SSS, you must check each possible proportion of the side lengths of a triangle.

Not similar

Use SSS to find the Scale Factor and determine whether the triangles are similar…if they are similar name the triangles correctly

DFAC

EFBC

DEAB

23

69

23

1015

23

812

∆ ABC ~∆DEF

Use SSS to find the Scale Factor and determine whether the triangles are similar

DEAB

DFAC

EFBC

45

78

67

Not Similar

Assuming that ∆ ABC~ ∆ DEF find x.Each proportion will equal the scale factor

EFBC

DFAC

DEAB

124

= )1(38x

4(3x+3) = 8(12)12x + 12 = 9612x = 84 x = 7

Assuming that ∆ XYZ~ ∆ PQR find x.Each proportion will equal the scale factor

QRYZ

PRXZ

PQXY

32

3020

)2(312

32

x

3(12) = 2(3x -6) 36 = 6x -1248 = 6x x = 8

Side Angle Side Similarity Theorem

• If 2 triangles have a corresponding congruent angle and the sides including that angle are proportional, then the 2 triangles are similar.

Are the Triangles similar?How?

yes

SAS

Name the corresponding Side, Angle, and Side for each triangle

53

3018

CDAC

DCEACB 53

159

CEBC

Are the Triangles similar?How?

yes

SAS

Name the corresponding Side, Angle, and Side for each triangleFind the scale factor to back it up

34

1824

PNSR

NR 34

2128

NQRT

Are the Triangles similar?How?

yesSAS or SSS

Name the corresponding Side, Angle, and Side and Side, Side, Side for each triangle. Find the scale factor to back it up

34

1520

XYWX XZYWZX

34

912

ZYXZ

34

1216

XZWZ

Find the Scale Factor and determine whether the triangles are similar using SAS

XYRS

YZST

32

64

32

96

∆ RST ~ ∆ XYZ

YS

Is there enough information to determine whether the triangles are similar?

no

Why?

The sides are not proportional and it does not follow SAS.

Is there enough information to determine whether the triangles are similar?

yesWhich Similarity Postulate

allows us to say yes? SAS

95

95

3620

2715

CFCG

CECD CC

Are the triangles similar? Which similarity postulate allows us to say it is similar?

yes

SAS

The sides are proportional and the included angles are congruent.

Are the triangles similar? Which similarity postulate allows us to say it is similar?

yes

SAS

2 sides are proportional and the included angle is congruent.

Assuming that these triangles are similar. Let’s solve for the missing variables.

4x - 5

3x + 8

6y + 11

13y - 38

15

12

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