6.5 – prove triangles similar by sss and sas
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6.5 – Prove Triangles Similar by SSS and SAS
Side-Side-Side Similarity (SSS~):
Two triangles are similar if the 3 corresponding side lengths are proportional
B
A
C E
D
F
DF
AC
EF
BC
DE
AB
Side-Angle-Side Similarity (SAS~):
Two triangles are similar if 2 corresponding sides are proportional and the included angle is congruent
EF
BC
DE
AB
B
A
C E
D
F
1. Verify that ABC ~ DEF. Find the scale factor of ABC to DEF.
ABC: AB = 12, BC = 15, AC = 9
DEF: DE = 8, EF = 10, DF = 6
B
A
C E
D
F
12
8
15
9
6
10
8
12
2
3
10
15
2
3
6
9
2
3
Scale Factor:2
3
2. Is either LMN or RST similar to ABC? Explain.
8
10
4
5
6
12
1
2
5
10
1
2
6
12
1
2
5
10
1
2ABC ~ RST by SSS~
3. Determine whether the two triangles are similar. If they are similar, write a similarity statement and find the scale factor of Triangle B to Triangle A.
4
16
1
4
3
12
1
4
L X
YES or NO
______ ~ ______
Scale Factor:
YXZ JLK
1
4
10
18
2
9
9
16
3. Determine whether the two triangles are similar. If they are similar, write a similarity statement and find the scale factor of Triangle B to Triangle A.
YES or NO
______ ~ ______
Scale Factor:
4. Determine whether the triangles are similar. If they are similar, state which postulate or theorem that justifies your answer. Show all work!
15
65
2
10
45
2
GKH NKM
SAS ~
4
106
15
YES or NOReason: ___________
ABC DEC
B E
YES or NOReason: ___________AA ~
4. Determine whether the triangles are similar. If they are similar, state which postulate or theorem that justifies your answer. Show all work!
16
24
2
3
28
36
7
9
YES or NOReason: ___________
4. Determine whether the triangles are similar. If they are similar, state which postulate or theorem that justifies your answer. Show all work!
∆HGJ ~ ∆HFKBy SSS~
#10
HW ProblemSecti
onPage # Assignment
Spiral
6.5 391-394 3-11, 15, 16, 33 (a & b only) 10 - 15
16.5
22
15
20
18
24
15
203
4
18
243
4
16.5
223
4
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