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

Answer:

Given:  

In ΔLMN and ΔXYZ,

 MN = 3, LN = 2, YZ = 9, XZ = 6

To find: criteria that needs to be shown to prove ΔLMN  ΔXYZ using SAS similarity theorem

Solution:

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,

$\frac{LN}{XZ}$ = $\frac{2}{6}$ = $\frac{1}{3}$

$\frac{MN}{YZ}$ = $\frac{3}{9}$ = $\frac{1}{3}$

THEREFORE, LN/XZ = MN/YZ

So, ΔLMN congruent to ΔXYZ by SAS similarity theorem if angle N CONGRUENT ANGLE Z

Answer 2

Answer:

∠N ≅ ∠Z

Step-by-step explanation:

Took test on Edge 2021