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

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flightbath flightbath · Answer 1 · 2019-01-11T12:49:54+01:00

Answer:

Option B is correct.

Step-by-step explanation:

We have given a triangle ABC and EDC please look at the figure

We can see that AE and BD are transversal therefore, ∠EAB=∠AED being alternate interior angles

And ∠ACB=∠DCE are vertically opposite angles hence, equal

So, by AA similarity postulate the above to triangles are similar

ΔABC [tex]\sim[/tex] ΔEDC

Therefore, Option B is correct that is Triangle ABC is similar to triangle EDC , because m∠3 = m∠4 and m∠1 = m∠5

NOTE: m∠3 = m∠4 corresponds to m∠ACB=m∠DCE

And m∠1 = m∠5 corresponds to m∠EAB=m∠AED