Question

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

AB and DE are parallel lines, and AE and BD are transversals. The transversals intersect at C. Angle CAB is labeled 1, angle ABC is labeled 2, angle ACB is labeled 3, angle DCE is labeled 4, angle CDE is labeled 6, and angle CED is labeled 5.

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


Triangle ABC is similar to triangle EDC , because m∠3 = m∠6 and m∠1 = m∠4
Triangle ABC is similar to triangle EDC , because m∠3 = m∠4 and m∠1 = m∠5
Triangle ABC is congruent to triangle EDC , because m∠3 = m∠4 and m∠1 = m∠5
Triangle ABC is congruent to triangle EDC, because m∠3 = m∠6 and m∠61 = m∠4

Answer 1

Triangle ABC is similar to triangle EDC , because m∠2 = m∠6 and m∠1 = m∠5

Explanation:

Nothing indicates any triangle sides are congruent, a necessary condition for the triangles to be congruent.

In triangles ABC and EDC, angles 1 and 5 are corresponding. They are "alternate interior angles" with respect to the transversal AE, so are congruent. Angles 2 and 6 are congruent for a similar reason. The vertical angles at C are congruent, so the triangles are similar.

Triangle ABC is similar to triangle EDC , because m∠2 = m∠6 and m∠1 = m∠5.