Kayla wants to find the width, AB, of a river. She walks along the edge of the river 90 ft and marks point C.
Then she walks 72 ft further and marks point D. She turns 90° and walks until her location, point A, and point
Care collinear. She marks point E at this location, as shown.

(a) Can Kayla conclude that AABC and AEDC are similar? Why or why not?
(b) Suppose DE = 54 ft. What is the width of the river? Round to the nearest foot. Provide all work.
d States

Part a) Triangles ABC and CDE are similar by AAA

Part b) The width of the river is 68 feet

Step-by-step explanation:

Part a)

we know that

If two figures are similar, then the ratio of its corresponding sides is equal and its corresponding angles are congruent

In this problem , triangles ABC and CDE are similar by AAA, because its corresponding angles are congruent

so

Part b)

Remember that

If two figures are similar, then the ratio of its corresponding sides is equal and is called the scale factor

so

substitute the values and solve for AB (the width of the river)