Question

two triangle are congruent if two angles and the included side of one triangle are equal to two angles and the included side of other triangle.
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Answer 1

ASA Congruence Rule: If two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, then the two triangles are congruent (ASA Congruence Rule).

Construction: Two triangles are given as follows in which:

∠ABC=∠DEF

and ∠ACB=∠DEF

Sides AB=DE

To prove: ΔABC≅ΔDEF

Proof:

∠ABC=∠DEF (given)

AB=DE

AC=DF (Sides opposite to corresponding angles are in the same ratio as ratio of angles)

Hence, ΔABC≅ΔDEF (SAS rule)

congruency of triangles 2 congruency of triangles 3

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