Congruencies and Proportions in Similar Triangles

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Congruencies and Proportions in Similar Triangles

• Lesson 8.4

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If we know that two triangles are congruent, we
can use the definition of congruent triangles
(CPCTC) to prove that pairs of angles and sides
are congruent.
Likewise, if two triangles are similar, we can
use the definition of similar polygons to prove
that

1. Corresponding sides of the triangles are
   proportional. (The ratios of the measures of
   corresponding sides are equal)
2. Corresponding angles of the triangles are
   congruent.

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Given BD CE Prove AB CE AC BD
Since BD is parallel to CE, ltABD congruent to
ltACE (corr lt) ltADB congruent to ltAEC (corr
lt) ?ABD ?ACE (AA)
Corr. Sides ratio

AB CE AC BD means extremes
4
Mr. Bunny is nine feet away from a flag pole that
is 15 feet high. If Mr. Bunnys shadow is 2.5 ft
long, and touches the end of the shadow of the
flag pole, how tall is the bunny?
HINT draw the picture set up
proportions solve
15 ft.
x ft.
9 ft.
2.5 ft.
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Set up proportions

• Corresponding parts
• (height to height, shadow to shadow) OR
• Actual to shadow

or


Which one will you use? Solve.
The bunny is about 3.26 ft tall.