7.4. Similarity by SSS and SAS http://www.ck12.org
Example 4:Are there any similar triangles? How do you know?
Solution:^6 Ais shared by 4 EABand 4 DAC, so it is congruent to itself. IfAEAD=ABACthen, by SAS Similarity, the
two triangles would be similar.
9
9 + 3
=
12
12 + 5
9
12
=
3
4
6 =
12
17
Because the proportion is not equal, the two triangles are not similar.
Example 5:From Example 4, what shouldBCequal for 4 EAB∼4DAC?
Solution:The proportion we ended up with was 129 =^346 =^1217 .ACneeds to equal 16, so that^1216 =^34. Therefore,
AC=AB+BCand 16= 12 +BC.BCshould equal 4 in order for 4 EAB∼4DAC.
Similar Triangles Summary
Let’s summarize what we’ve found that guarantees two triangles are similar.Two triangles aresimilarif and only if:
TABLE7.2:
Name Description Picture
AA Two angles in one triangle are con-
gruent to two angles in another tri-
angle.SSS for Similar Triangles All three sides in one triangle are
proportional to three sides in an-
other triangle.SAS for Similar Triangles Two sides in one triangle are pro-
portional with two sides in another
triangle AND the included angles
are congruent.