Download Geometry8.3

Section 8.3
Warm-Up Problems
Find the ratio of x:y
7
5

x  3y x  2 y
Find the fourth proportional to 2, 4, and 18.
Find the mean proportional to 4 and 36.
Section 8.3 Proving Triangles Similar
By the end of this lesson you will be able to:
•Show demonstrated ability with previous material
•Use several methods to prove that triangles are
similar
Similar Triangles Notation
~
ΔABC ~ DEF
“Triangle ABC is similar to triangle DEF.”
similar to
A
D
12
8
4
6
F
E
B
10
C
5
Postulate:
If there exists a correspondence between the vertices of two
triangles such that the three angles of one triangle are
congruent to the corresponding angles of the other triangle,
then the triangles are similar. (AAA)
Theorem:
If there exists a correspondence between the vertices of two
triangles such that the two angles of one triangle are
congruent to the corresponding angles of the other, then the
triangles are similar. (AA)
Theorem:
If there exists a correspondence between the vertices of two
triangles such that the ratios of the measures of
corresponding sides are equal, then the triangles are similar.
(SSS~)
Theorem:
If there exists a correspondence between the vertices of two
triangles such that the ratios of the measures of two pairs of
corresponding sides are equal and the included angles are
congruent, then the triangles are similar. (SAS~)
Always, Sometimes, Never
•If two triangles are similar, then they are congruent.
•SOMETIMES
•If two triangles are congruent, then they are similar.
•ALWAYS
•An obtuse triangle is similar to an acute triangle.
•NEVER
•Two right triangles are similar.
•SOMETIMES
•Two equilateral polygons are similar.
•SOMETIMES
•Two equilateral triangles are similar.
•ALWAYS
•Two rectangles are similar if neither is a square.
•SOMETIMES
Homework
Section 8.3
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