Question

What condition would prove triangle JKL is similar to triangle XYZ

Answer 1

Two triangles are similar when they have the same measure for their angles and proportional corresponding sides.

In this case, we have two triangles which have one pair of congruent angles ($\frac{LK}{ZY}=\frac{56}{7}=8$Then, the proportions for the other pair of corresponding sides have to be equal to 8.

Then, we can find the other corresponding pairs:

One is the other adyacent side to L, that is LJ, that will correspond to the the other adyacent side of The other pair remaining is the opposite side to

Then, we can write:

$\frac{LJ}{ZX}=\frac{JK}{YX}=\frac{LK}{ZY}=8$

Options A and B are not correct, as the proportion written that way should be 8 and not 1/8.

Option C is already given in the picture, so it does not add information.

Option D is correct, because it add a pair of proportional corresponding sides and with another pair of corresponding proportional sides and a pair of congruent angles, is enough information to prove that the triangles are similar.

Answer: Option D (JL/XZ = 8)