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Lesson 6-3
Similar
Triangles
Ohio Content
Standards:
Ohio Content
Standards:
Describe and apply the properties of
similar and congruent figures; and
justify conjectures involving similarity
and congruence.
Ohio Content
Standards:
Make and test conjectures about
characteristics and properties (e.g.,
sides, angles, symmetry) of twodimensional figures and threedimensional objects.
Ohio Content
Standards:
Use proportions in several forms to
solve problems involving similar
figures (part-to-part, part-to-whole,
corresponding sides between
figures).
Ohio Content
Standards:
Use proportional reasoning and apply
indirect measurement techniques, including
right triangle trigonometry and properties
of similar triangles, to solve problems
involving measurements and rates.
Ohio Content
Standards:
Apply proportional reasoning to solve
problems involving indirect
measurements or rates.
Postulate 6.1
Angle-Angle (AA)
Similarity
Postulate 6.1
Angle-Angle (AA)
Similarity
If the two angles of one triangle
are congruent to two angles of
another triangle, then the
triangles are similar.
Theorem 6.1
Side-Side-Side
(SSS) Similarity
Theorem 6.1
Side-Side-Side
(SSS) Similarity
If the measures of the
corresponding sides of two
triangles are proportional, then
the triangles are similar.
Theorem 6.2
Side-Angle-Side
(SAS) Similarity
Theorem 6.2
Side-Angle-Side
(SAS) Similarity
If the measures of two sides of
a triangle are proportional to
the measures of two
corresponding sides of another
triangle and the included
angles are congruent, then the
triangles are similar.
In the figure, AB DC ,
BE  27, DE  45, AE  21,
and CE  35. Determine
which tria ngles in the figure
are similar.
C
B
E
A
D
Given RS UT ,
RS  4, RQ  x  3,
QT  2 x  10, UT  10,
find RQ and QT .
4
R
x+3
S
Q
2x + 10
U
10
T
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 the Sears Tower’s shadow and it
was 242 feet at that time. What is
the height of the Sears Tower?
Assignment:
Pgs. 302-306
10-20 evens,
51-61 odds