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Transcript 
Geometry
Sources:
Discovering Geometry (2008) by Michael Serra
Geometry (2007) by Ron Larson
ï‚žWe
define similar triangles in
Geometry as triangles having the
same shape; specifically having
congruent corresponding angles
and proportional corresponding
sides.
Are the two triangles similar?
5
7
6
15
21
Yes they are!
Scale factor is 3!
Because the triangles
are similar, the
corresponding angles
are congruent!
18
AA
Similarity
Postulate
ï‚ž
If two angles of a triangle are congruent
to two angles of another triangle, then the
two triangles are similar.
Are the two triangles similar ?
ÐABE @ ÐACD
ÐA @ ÐA
therefore
DABE ~ DACD
by AA Sim. Post.
Are the two triangles similar ?
ÐS @ ÐU
ÐR @ ÐT
therefore
DSVR ~ DUVT
by AA Sim. Post.
SSS
Similarity
Conjecture
ï‚ž
If the ratios of the 3 pairs of
corresponding sides of two triangles are
equal, then the two triangles are similar.
Are the two triangles similar ?
All 3 pairs of sides have equal ratios!
Therefore the two triangles are similar!
Are the two triangles similar ?
All 3 pairs of sides have equal ratios!
Therefore the two triangles are similar!
SAS
Similarity
Conjecture
ï‚ž
If the ratios of 2 pairs of corresponding
sides of two triangles are equal, and the
included angles are congruent, then the
two triangles are similar.
Are the two triangles similar ?
Yes they are similar by SAS Similarity Conj.
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