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Geometry Lesson 6-5: Prove Triangles Similar by SSS and SAS
Learning Target: By the end of today’s lesson we will be able to successfully use the SSS and SAS Similarity
Theorems.
Side-Side-Side (SSS) Similarity Theorem:
If the corresponding side lengths of two triangles are ____________________,
then the triangles are similar.
If
AB BC CA


, then ABC ~ RST.
RS
ST TR
Example 1: Is either DEF or GHJ similar to ABC?
Example 2: Find the value of x that makes ABC ~ DEF.
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 ______________, then
the triangles are similar.
If X  M , and
ZX
XY

, then XYZ  MNP.
PM MN
Example 3: Marco is drawing a design for a birdfeeder. Can he construct
the top so it is similar to the bottom using the angle measure
and lengths shown?
Triangle Similarity Postulate and Theorems:
AA Similarity Postulate: If A  D and B  E, then ABC ~ DEF.
SSS Similarity Theorem: If
AB BC AC


, then ABC ~ DEF.
DE EF DF
SAS Similarity Theorem: If A  D and
AB AC

, then ABC  DEF.
DE DF
Example 4: Tell what method you would use to show that the triangles are similar.
a.)
b.)