Question

Given that lines AB and DE are parallel,determine how triangles ABC and EDC can be shown to be similar

Answer 1

Explanation:

Draw the two triangles so the two triangles share point C. It should look like a bowtie.

(1) AB is parallel to DE Given

(2) Angle A = Angle D If two parallel lines are cut by a transversal, alternate interior angles are equal.

Angle B = Angle E

(3) Angle BCA = Angle DCE Vertical angles are equal.

(4) Triangle BAC is similar to Triangle DEC If 3 angles in one triangle are equal to three angles in another triangle, the triangles are similar.

(5) AB/DE = AC/EC If two triangles are similar, corresponding sides are proportional.

Answer 2

The transversals cutting through the parallel lines create angles that are congruent to one another. Angles 1`and 5 are alternate interior and are congruent. Angles 2 and 6 are alternate interior and are congruent. And of course if 2 of 3 angles in 2 triangles are congruent, then the 3rd angles have to be congruent as well. HOWEVER, we can see that the sides are NOT congruent, and we need at least one side to prove congruency. Since we have 3 congruent angles, we can only say they are similar.

Explanation: