Question

In ∆XYZ and ∆LMN, ∠Y ≅ ∠M, ∠Z ≅ ∠N, State the test by which the two triangles ∆XYZ and ∆LMN are similar.

SAS test of similarity.
AA test of similarity.
SSS test of similarity.
None of these above

please give me correct ans
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Answer 1

$\huge \rm \bf{QUESTION}$

In ∆XYZ and ∆LMN, ∠Y ≅ ∠M, ∠Z ≅ ∠N, State the test by which the two triangles ∆XYZ and ∆LMN are similar.

$\red{\frac{XY}{ \:LM} = \frac{ \: YZ}{ \: MN} = \frac{ \:XZ}{ LN }}$

$\sf <X=<L,<Y=<M \: and \\ \sf<Z=<N$

Answer 2

Given : In ∆XYZ and ∆LMN, ∠Y ≅ ∠M, ∠Z ≅ ∠N

To Find : State the test by which the two triangles ∆XYZ and ∆LMN are similar.

SAS test of similarity.

AA test of similarity.

SSS test of similarity.

None of these above

Solution:

In ∆XYZ and ∆LMN

∠Y ≅ ∠M,

∠Z ≅ ∠N

Angle-Angle Similarity (AA~) Theorem

If two angles of one triangle and two angles of another triangle have the same measures, then the triangles are similar.

Hence two triangles ∆XYZ and ∆LMN are similar using AA test of similarity.

SAS test of similarity.

If an angle of one triangle and an angle of another triangle have the same measure, and the sides containing those angles are proportional, then the triangles are similar.

But no information given about sides

SSS test of similarity.

If the sides of one triangle and the corresponding sides of another triangle are proportional, then the triangles are similar.

But no information given about sides

Hence correct answer is  AA test of similarity.

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