Page 162 - ArithBook5thEd ~ BCC
P. 162
Corresponding sides of similar triangles are proportional:
If: ∠A = ∠D, ∠B = ∠E,and ∠C = ∠F,
E
B
A C
D F
BC AC AB
Then: = = .
EF DF DE
Example 203. The triangles below are similar, with ∠D = ∠A, ∠E = ∠B and ∠F = ∠C. AB =
15 feet, BC =12 feet, and DE =22.5 feet. Find EF.
D
A
15 ft. C
22.5 ft.
F
12 ft.
B
x ft.
E
Solution. The ratios of the corresponding sides opposite ∠F = ∠C ( DE ) and the corresponding sides
AB
opposite ∠D = ∠A ( EF ) are equal:
BC
DE EF
= .
AB BC
Filling in the given information, and using x to represent the unknown side length EF,we have
22.5 x
=
15 12
(22.5)(12) = 15x
270 = 15x
270
x = =18.
15
EF =18 feet.
We now describe two ways of obtaining a pair of similar triangles. Both involve the notion of parallel
line segments. Two line segments are parallel if they do not cross, even if extended infinitely in either
direction (think of straight train tracks).
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