Transcript 8.3 Methods of Proving Triangles Similar

8.3 METHODS OF PROVING
TRIANGLES
SIMILAR
AAA
 In order to prove triangles are similar we need to start with a
Postulate.
• AAA: If three angles correspond to the other triangle’s three angles,
then the triangles are
similar.
AA
 The following are theorems that will be used in proofs.
• AA: If two corresponding angles of one triangle correspond to the
other two angles of the other triangle, then the triangles are similar.
Ex: G: <A congruent <D
<B congruent <E
C:
ABC = DEF
SSS~
 SSS~ :If the three sides of the triangles are proportional then the
triangles are similar.
Ex:
G:
Prove: ABC ~ DEF
SAS~
 SAS~ : If two of the triangles sides are proportional and the
included angles are congruent, then the two triangles are similar.
Ex: G: <B = <E
P:
ABC ~ DEF
CPCTC
 If you are given the two triangles are similar, then
• 1. Corresponding sides of the triangles are proportional (The ratios
of the measures of corresponding sides are equal.)
• 2. Corresponding angles of the triangles are congruent.