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

A) ∠N ≅ ∠Z

Explanation:

Answer 2

∠N ≅ ∠Z

Explanation:

In the Side-Angle-Side (SAS) similarity theorem, the included angle of the two given sides of a triangle is also given. This theorem relates two legs of a triangle with the angle formed by the legs.

Comparing the sides of △LMN and △XYZ, it would be observed that the corresponding sides of △XYZ has a scale of 3. So to prove that △LMN ~ △XYZ by the SAS similarity theorem, it would be required to also show that ∠N ≅ ∠Z.