Question

Write the conditions of congruency of two triangles.
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Answer 1

$\huge\pink{\mathfrak{answer}}$

If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. This is an extension of ASA.

Answer 2

Congruence

Two Triangles are said to be congruent if ,

$\red\bigstar$ All Sides are Equal

             and

$\red\bigstar$ All Angles are Equal

Congruence is represented by the Symbol ' ≅ '

Conditions of Congruence of Two Triangles are :

SAS Congruence ( Side Angle Side Congruency )  

If the two sides and the included angle of one triangle are equal to the two sides and the included angle  of another triangle the triangles are congruent by SAS rule of Congruence.

SSS Congruence ( Side Side Side Congruency )  

If  three sides of a triangle are equal to three sides of another triangle, the triangles are congruent by SSS rule of Congruence .

ASA Congruence ( Angle Side Angle )

If Two angles and the corresponding side of a triangle is equal to the two angles and the corresponding side  , the triangles are congruent by ASA rule of Congruence .

AAS Congruence (Angle Angle Side )

If two angles and a non-included side of one triangle are equal to two angles and the  non-included side of another triangle, then the two triangles are congruent by AAS rule of Congruence .

RHS Congruence

If the length of the hypotenuse and one side of one triangle, is equal to the length of the hypotenuse and corresponding side of the other triangle, then the two triangles are congruent by RHS ruleof Congruence  .

[ Only Applicable for right angled Triangle ]