Question

In the diagram, the ratios of two pairs of corresponding sides are equal.

Triangles L M N and X Y Z are shown. Side L M is blank, side M N is 3, and side N L is 2. Side X Y is blank, side Y Z is 9, and side Z X is 6.

To prove that △LMN ~ △XYZ by the SAS similarity theorem, it also needs to be shown that

∠N ≅ ∠Z
∠N ≅ ∠X
∠L ≅ ∠Z
∠L ≅ ∠Y

Answer 1

∠N ≅ ∠Z

Reason: the equal ratios are for MN ↔ YZ and NL ↔ ZX, which are the two sides that meet at N in △LMN and at Z in △XYZ. For SAS similarity you must show the included angles are congruent, i.e. ∠N ≅ ∠Z.