Download 623Notes 12.8-9

Math 623
Mr. Kadish
Notes for section 12.8/9
The rules for determining similarity between triangles are related to the rules for
determining congruence.
Triangle Congruence Theorem
Triangle Similarity Theorem
SSS
SSS*
SAS
SAS
ASA
AAS
AA
* Where in the congruence theorems, S represents a pair of congruent
sides, for similarity theorems it designates a ratio of corresponding sides.

SSS Similarity Theorem: If the 3 sides of one triangle are proportional to the 3
sides of a second triangle, then the triangles are similar.

AA Similarity Theorem: If two triangles have two angles of one congruent to
two angles of the other, then the triangles are similar.

SAS Similarity Theorem: If, in two triangles, the ratio of two pairs of
corresponding sides are equal and the included angles are congruent, then the
triangles are similar.
Similarity Statement
For our purposes in math 623, we will not be proving similarity using traditional or “two
column” proofs. However, we will show similarity by providing a similarity statement, in
addition to identifying the appropriate similarity theorem: SSS, ASA or AA. To do this
we identify the ratios of lengths of corresponding sides and show that the ratios are
equal to each other and to the ratio of similitude (eg. scale change factor or magnitude).
Example:
B
A
6
100
C
E
20
100
15
8
D
ABC~FED by S.A.S.
FD = DE = EF = 2.5
AB
BC
CA
F