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
Page 391
• #3- 9, 15 - 23