Question

Kayla wants to find the distance, AB, across a river. She walks along the edge of the river 100 ft and marks point C. Then she walks 100 ft further and marks point D. She turns 90° and walks until her location, point A, and point C are collinear. She marks point E at this location, as shown. (a Can Kayla conclude that ABC and EDC are congruent? Why or why not?
(b) Suppose DE=175 ft. What can Kayla conclude? Explain.

Answer 1

You are given Kayla's walking distance along the edge of the river 100 ft and marks point C, then she walks 100 ft further and marks point D and she turns 90° and walks until her location, point A, and point C are collinear. She marks point E at this location. ABC and EDC are congruent.

Answer 2

Answer:

The triangles ABC and EDC are congruent by ASA rule.

Step-by-step explanation:

Given Kayla walks along the edge of the river 100 ft and marks point C. Then she walks 100 ft further and marks point D. She turns 90° and walks until her location, point A, and point C are collinear. She marks point E at this location. we have to find the distance AB.

In ΔABC and ΔEDC

∠EDC=∠ABC    (each 90)

CD=CB              (given)

∠DCE=∠BCA    (vertical angles)

By ASA rule, ΔABC≅ΔEDC

Now, given DE=175 ft

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

By triangle proportionality,

$\frac{BC}{DC}=\frac{AB}{DE}$

⇒ $\frac{100}{100}=\frac{AB}{175}$

⇒ AB=175 ft.

Length of DE is same as AB