n 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

According to SAS Similarity Theorem, if two sides in one triangle are proportional to two sides in another triangle and the included angle between the sides are congruent, then the two triangles are said to be similar.

In ΔLMN and ΔXYZ,

[tex]\frac{LN}{XZ}=\frac{2}{6}=\frac{1}{3}\\\frac{MN}{YZ}=\frac{3}{9}=\frac{1}{3}\\\therefore \frac{LN}{XZ}=\frac{MN}{YZ}[/tex]

So, ΔLMN [tex]\sim[/tex] ΔXYZ by SAS similarity theorem if [tex]\angle N\cong \angle Z[/tex]

akposevictor akposevictor · Answer 2 · 2021-12-22T19:45:23+01:00

For both triangles to be proven to be similar by the SAS similarity theorem, the additional information needed to be shown is a pair of congruent included angles, which is: a. ∠N ≅ ∠Z

What is the SAS Similarity Theorem?

The SAS Similarity Theorem states that two triangles are similar to each other if they have two pairs of corresponding sides that are proportional to each other and a pair included angles that are congruent.

△LMN and △XYZ have:

two pairs of corresponding sides that are proportional (YZ/MN = XZ/LN = 3)

Therefore, for both triangles to be proven to be similar by the SAS similarity theorem, the additional information needed to be shown is a pair of congruent included angles, which is: a. ∠N ≅ ∠Z

Learn more about the SAS Similarity Theorem on:

https://brainly.com/question/12960403