7.3 Triangle Similarity: AA, ASA, SSS
Objectives:
G.SRT.5: Use congruence and similarity criteria for triangles to solve problems and prove
relationships in geometric figures.
G.SRT.3: Use the properties of similarity transformations to establish the AA criterion for
two triangles to be similar.
G.SRT.2: Given two figures, use the definition of similarity in terms of similarity
transformations to decide if they are similar.
For the Board: You will be able to prove triangles are similar by using AA, SSS, and SAS.
Anticipatory Set:
According to the definition of Similar Figures, to be similar all the angles of one figure must be
congruent to all the angles of the other and all the sides must be proportional.
This is more than is necessary for triangles.
Angle-Angle (AA) Similarity Postulate
If two angles of the triangle are congruent to two angles of another triangle, then the two
triangles are similar.
Given: <A
<X, <B
<Y
Conclusion: ΔABC ~ ΔXYZ
Side-Side-Side (SSS) Similarity Theorem
If the lengths of the corresponding sides of two triangles are proportional, then the triangles
are similar.
Given:
XZ
AC
YZ
BC
XY
AB
Conclusion: ΔABC ~ ΔXYZ
Side-Angle-Side (SAS) Similarity Theorem
If an angle of one triangle is congruent to an angle of a second triangle and the lengths of
the sides including these angles are proportional, then the triangles are similar.
Given: <B
<Y,
YZ
BC
XY
AB
Conclusion: ΔABC ~ ΔXYZ
B
A
X
Y
C
Z
B
A
X
Y
C
Z
B
A
X
Y
C
Z
