Warm UP• Given that the following
two pentagons are similar, find x.
x4
6
7
5
12 8
414
10
Objective• SWBAT use the AAA, SAS
and SSS similarity postulates to decide which triangles are similar and find unknowns.
Homework
• P. 433 – 434: # 5 – 9, 12 – 19
Congruence vs. Similarity
• The match of the century!
• Who will win?
Congruence vs. Similarity
• Congruence implies that all angles and sides are equal/identical whereas...
Congruence vs. Similarity
•Similarity implies that only the angles are congruent and the sides are proportional
Congruence vs. Similarity
• What can be congruent?
• What can be similar?
Back to Triangles
• Since we talked about congruent triangles so much, we should mention similar triangles.
Back to Triangles• How could triangles be
congruent?
• SSS
• SAS
• ASA
AAS
HL
SSS Similarity Postulate
• Two triangles are similar if all three pairs of corresponding sides are proportional.
SSS Similarity Postulate
A
B
C D
E
F7
219 2713
39
SSS Similarity Postulate
•∆ABC ~ ∆EDF
SAS Similarity Postulate
• Two triangles are similar if two pairs of corresponding sides are proportional and the included angle is congruent
SAS Similarity Postulate
A
B
C D
E
F4 6
8 12
SAS Similarity Postulate
•∆ABC ~ ∆FED
AAA Similarity Postulate
• Two triangles are similar if two pairs of corresponding angles are congruent
AA Similarity Postulate
A
B
C D
E
F
AA Similarity Postulate
•∆ABC ~ ∆FED
Example
•∆APE ~ ∆DOG. If the perimeter of ∆APE is 12 and the perimeter of ∆DOG is 15 and OG = 6, find the PE.
Conclusion
•Congruence vs. Similarity
•AAA~
•SAS~
•SSS~
Practice 10-2•Answer Example sets 2 and 3.
•Be sure to include the similarity statement.
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