Question

The figure shows two parallel lines AB and DE cut by the transversals AE and BD:

Which statement best explains the relationship between Triangle ABC and Triangle EDC ?

A. Triangle ABC is similar to triangle EDC , because m∠2 = m∠6 and m∠1 = m∠5
B. Triangle ABC is similar to triangle EDC , because m∠3 = m∠6 and m∠1 = m∠4
C. Triangle ABC is congruent to triangle EDC , because m∠3 = m∠4 and m∠1 = m∠5
D. Triangle ABC is congruent to triangle EDC , because m∠3 = m∠6 and m∠1 = m∠4

Answer 1

The answer is A. 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. Hence, the answer being A.