Proving that Triangles are Similar
Not only can proportions be used to solve for missing sides when it is known
that two triangles are similar, but conversely, proportions can be used to
determine if two triangles are similar. There are three different postulates,
or tests, that prove similarityin triangles. These postulates investigate the
measurements of corresponding angles as well as the proportions of corre-
sponding sides in triangles. If two triangles satisfy any of these three pos-
tulates, then they are similar. Here are the three tests of similarity:
Test 1: Angle-Angle (AA) Postulate: If two angles of one triangle are
congruent to two angles of another triangle, then the triangles are similar.
This is true because two angles really prove that all three angles are equal,
since their sum needs to be 180°.
BA CGFE501 Geometry Questions