CONGRUENCIES AND
PROPORTIONS IN SIMILAR
TRIANGLES
Lesson 8.4
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.
A
Given: BD ║ CE
B
Prove: AB · CE = AC · BD
C
Since BE is parallel to CE,
<ABD congruent to <ACE (corr <)
<ADB congruent to <AEC (corr <)
 ΔABD ~ΔACE (AA~)
Corr. Sides = ratio
AB
BD
=
AC
CE
AB · CE = AC · BD
means extremes
D
E
Mr. Bunny is nine feet away from a flag pole that is
15 feet high. If Mr. Bunny’s 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.
SET UP PROPORTIONS:


Corresponding parts
(height to height, shadow to shadow) OR
Actual to shadow
15
x
=
11.5
2.5
or
15
11.5
=
Which one will you use? Solve.
The bunny is about 3.26 ft tall.
x
2 .5