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Advanced Geometry
Similarity
Lesson 3
Triangle Similarity
In the Triangle Congruence unit we talked about four
tests for proving that two triangles are congruent;
SSS Congruence,
SAS Congruence,
ASA Congruence, and
AAS Congruence.
There are also tests to prove that two TRIANGLES are
similar:
AA Similarity,
SSS Similarity, and
SAS Similarity
AA Similarity
Two pairs of corresponding angles are CONGRUENT.
SSS Similarity
Three pairs of corresponding sides are PROPORTIONAL.
SAS Similarity
Two pairs of corresponding sides are PROPORTIONAL
and
the included angles are CONGRUENT.
EXAMPLES:
Determine whether each pair of triangles is similar.
Justify your answer.
Yes;
AA Similarity
No;
Correpsonding
sides are not
proportional.
No;
There is not
enough
information.
EXAMPLE:
Given
UTQ SRQ and RS || UT ,
RS = 4, RQ = x + 3, QT = 2x + 10,
and UT = 10. Find RQ and QT.
EXAMPLE:
Josh wanted to measure the height of the Sears Tower
in Chicago. He used a 12-foot light pole and measured
its shadow at 1 p.m. The length of the shadow was 2 feet.
Then he measured the length of Sears Tower’s
shadow and it was 242 feet at the same time.
What is the height of the Sears Tower?
EXAMPLE:
Triangles KLJ and MNJ have vertices
J (2, 2), K (5, 4), L(5, 5), M (4, 2),and N (4, 4).
Justify that
KLJ
MNJ .
EXAMPLE:
Simplify
252
.
90