Download Triangle Similarity Toolkit Angle-Angle Similarity Theorem (AA

Triangle Similarity Toolkit
Angle-Angle Similarity Theorem (AA~)
AA~ If two triangles have two pairs of
corresponding angles that have the same
measure, then the triangles are similar.
A  D and B  E therefore ABC DEF
Side-Angle-Side Similarity Theorem (SAS~)
SAS~ If two triangles have two pairs of
corresponding sides that are proportional and
the angles between them have the same
measure, then the triangles are similar.
8.4
12.2
 2 , U  A , and
 2 therefore RUN
4.2
6.1
CAT
Side-Side-Side Similarity Theorem (SSS~)
SSS~ If two triangles have all three pairs of
corresponding sides that are proportional
(this means that the ratios of corresponding
sides are equal), then the triangles are
similar.
12
9
6
 1.5 ,  1.5 , and  1.5 therefore ABC DEF
8
6
4
Similar triangles have the same angle measurements and all of their
sides have the same proportional ratio.
If the corresponding sides have a ratio of 1, then the triangles are
congruent.