Allie Terrell

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Allie Terrell Katie CooperAdvanced
Geometry3rd periodMs. Thompson
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LEARNING TARGET

• I can use triangle similarity to solve unknown
  sides and angles.

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VOCABULARY

• Similar two shapes are similar if they have the
  same number of sides, the same number of angles,
  and the same angle measure.

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Similar triangles are triangles that have the
same shape but not necessarily the same size.
?ABC ? ?DEF
?A ? ?D
?B ? ?E
?C ? ?F
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Six of those statements are true as a result of
the similarity of the two triangles. However, if
we need to prove that a pair of triangles are
similar how many of those statements do we need?
Because we are working with triangles and the
measure of the angles and sides are dependent on
each other, we do not need all six. There are
three special combinations that we can use to
prove similarity of triangles.
1. SSS Similarity Theorem ? 3 pairs of
proportional sides
2. SAS Similarity Theorem ? 2 pairs of
proportional sides and congruent angles between
them
3. AA Similarity Theorem ? 2 pairs of
congruent angles
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1. SSS Similarity Theorem ? 3 pairs of
proportional sides
?ABC ? ?DFE
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2. SAS Similarity Theorem ? 2 pairs of
proportional sides and congruent angles between
them
m?H m?K
?GHI ? ?LKJ
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The SSA Similarity Theorem does not work. The
congruent angles should fall between the
proportional sides (SAS). For instance, if we
have the situation that is shown in the diagram
below, we cannot state that the triangles are
similar. We do not have the information that we
need.
Angles I and J do not fall in between sides GH
and HI and sides LK and KJ respectively.
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3. AA Similarity Theorem ? 2 pairs of
congruent angles
m?N m?R
?MNO ? ?QRP
m?O m?P
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It is possible for two triangles to be similar
when they have 2 pairs of angles given but only
one of those given pairs are congruent.
m?T m?X
m?S m?Z
m?S 180?- (34? 87?)
?TSU ? ?XZY
m?S 180?- 121?
m?S 59?
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Sage and Scribe

• Work with your partner. Only one paper per
  partner.
• Page 483 10-26 and 40-46 (EVEN ONLY)
• Page 492 2- 14 (EVEN ONLY)

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REFERENCES

• www.dictionary.com
• paccadult.lbpsb.qc.ca/eng/extra/img/Similar20Tria
  ngles.ppt
• www.mente.elac.org/presentations/sim_tri_I.pps