6.4 – prove triangles similar by aa
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6.4 – Prove Triangles Similar by AA. AA Similarity (AA ~). Two triangles are similar if two of their corresponding angles are congruent. Use the diagram to complete the statement. GHI. Use the diagram to complete the statement. GI. HI. GH. - PowerPoint PPT PresentationTRANSCRIPT
6.4 – Prove Triangles Similar by AA
AA Similarity (AA ~)
Two triangles are similar if two of their corresponding angles are congruent.
Use the diagram to complete the statement.
______~MON GHI
Use the diagram to complete the statement.
???
MOONMN
GI HI GH
Use the diagram to complete the statement.
10
?
12
16
x
Use the diagram to complete the statement.
y
?
16
12 8
Use the diagram to complete the statement.
10
?
12
16
x
12x = 160
x = 40 3
Use the diagram to complete the statement.
12y = 128
x = 32 3
y
?
16
12 8
Use the diagram to complete the statement.
______~ABC DEF
?
?
?
CA
EF
AB
Use the diagram to complete the statement.
DE
BC
FD
_____B
Use the diagram to complete the statement.
E
Use the diagram to complete the statement.
?
8
12
?
x
y
Use the diagram to complete the statement.
?
6
12
?
x
16
Use the diagram to complete the statement.
16
6
12
?
x
16x = 72
x = 4.5
Use the diagram to complete the statement.
y
8
16
6
6y = 128
x = 64 3
Determine whether the triangles are similar. If they are, explain
why and write a similarity statement.
No
26°
47°
Determine whether the triangles are similar. If they are, explain
why and write a similarity statement.
AA~
ABC ~ EDC
ABC CDE
ACB ECD
Yes,
Determine whether the triangles are similar. If they are, explain
why and write a similarity statement.
AA~ABC ~ DEF
77°55°
B E
C F
Yes,
Determine whether the triangles are similar. If they are, explain
why and write a similarity statement.
No 82°
72°
Determine whether the triangles are similar. If they are, explain
why and write a similarity statement.
AA~
SRV ~ TRU
U SVR
T VSR
Yes,
Determine whether the triangles are similar. If they are, explain
why and write a similarity statement.
AA~
XTR ~ KAJ
T A
R J
Yes,
Find the length of BC.
4
7
7x = 20
x = 20 7
5
x
Find the value of x.
4
5
4x = 70
x = 17.5410
14
x
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~
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 XYes, SAS ~
YXZ ~ JLKScale Factor:
1
4
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.
10
18
2
9
9
16
L Z
No
Are the triangles similar? Explain your reasoning.
4
8
1
2
5.3
7
1
2
GKH NKM
Yes, SAS ~
Are the triangles similar? Explain your reasoning.
ABC DEC
Yes, AA ~
B E
Are the triangles similar? Explain your reasoning.
16
24
2
3
28
36
7
9
No, PN
LK
NO
KM