Question

2.) you are trying to find the distance ab between two points on either side of a river. to help, you measure and construct two triangles with matching side lengths to create two congruent triangles: triangle dec and triangle abc. you measure the following distances: ed = 32 ft, ec = 32 ft, dc = 28 ft, ac = 28 ft, bc = 32 ft

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle DEC\cong\triangle ABC\) (by SSS - Side - Side - Side congruence criterion as \(ED = BC = 32\) ft, \(EC=AB = 32\) ft, \(DC = AC=28\) ft), the corresponding sides of congruent triangles are equal.

Step2: Find the length of \(AB\)

The side \(AB\) corresponds to the side \(ED\) in the congruent triangles \(\triangle ABC\) and \(\triangle DEC\).

Answer:

\(AB = 32\) ft