Question

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

Answer 1

Answer:

Correct answer: A

Step-by-step explanation:

Answer 2

Answer:

$\angle N\cong \angle Z$

Step-by-step explanation:

Given:

In ΔLMN and ΔXYZ, $MN=3\,,\,LN=2\,,\,YZ=9\,,\,XZ=6$

To find: criteria that needs to be shown to prove ΔLMN $\sim$ 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,

$\frac{LN}{XZ}=\frac{2}{6}=\frac{1}{3}\\\frac{MN}{YZ}=\frac{3}{9}=\frac{1}{3}\\\therefore \frac{LN}{XZ}=\frac{MN}{YZ}$

So, ΔLMN $\sim$ ΔXYZ by SAS similarity theorem if $\angle N\cong \angle Z$