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Triangle Similarity:
Angle Angle
Recall
• Recall the definitions of the following:
• Similar
• Congruent
• Also recall the properties of similarity we discussed yesterday
• Corresponding angles in similar figures are congruent
• The ratio of corresponding sides in a figure are equal
There’s another way
• There are other ways to prove figures are similar
• Today we are looking at triangle similarity
• Mainly involving the angle-angle similarity postulate
Angle-Angle similarity postulate
• If two angles of one triangle are
congruent to two angles of another
triangle, then the two triangles are
similar
• This postulate allows you to say that
two triangles are similar if you know
that two pairs of angles are congruent.
• You don’t need to compare all of the
side lengths and angle measures to
show that two triangles are similar.
Third Angle Theorem
• If two angles in one triangle are
congruent to two angles in another
triangle, then the third angles must
be congruent also.
Using the AA similarity postulate
• Determine whether the triangles
are similar. If they are similar, write
a similarity statement. Explain your
reasoning.
Using the AA similarity postulate
• Are you given enough information
to show that ∆RST is similar to
∆RUV? Explain your reasoning.
Determine whether the triangles are similar. If they are similar, write a similarity
statement.
Using AA postulate to find the missing side