Question

guided practice
you just proved that (overline{ef}congoverline{eg}) using congruent triangles and cpctc.
if the officer knows the distance from (e) to (g), he can conclude that it is
the same distance from (e) to (f), which is the width of the river.
using congruent triangles: cpctc
type your answer and then click or tap done.
the officer stepped off 20 paces from (e) to (g). if his pace is (2\frac{1}{2}) ft long, how wide
was the river?
ft

Explanation:

Step1: Calculate the length of \(EG\)

The officer stepped off \(20\) paces from \(E\) to \(G\), and each pace is \(2\frac{1}{2}=\frac{5}{2}\) ft long.
Using the formula \(d = n\times l\) (where \(n = 20\) is the number of paces and \(l=\frac{5}{2}\) is the length of each pace), we have \(EG=20\times\frac{5}{2}\).

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Step2: Use \(EF\cong EG\) (by CPCTC)

Since \(EF\cong EG\) (corresponding parts of congruent triangles are congruent), and we found \(EG = 50\) ft.

Answer:

\(50\)