i 'If two sides of a triangle are congruent
then the angles opposite to them
are congruent prove
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If two angles of a triangle are congruent , then the sides opposite to these angles are congruent.
Proof
Draw SR¯¯¯¯¯ , the bisector of the vertex angle ∠PRQ .
Since SR¯¯¯¯¯ is the angle bisector , ∠PRS≅∠QRS .
By the Reflexive Property ,
RS¯¯¯¯¯≅RS¯¯¯¯¯
It is given that ∠P≅∠Q .
Therefore, by AAS congruent, ΔPRS≅ΔQRS .
Since corresponding parts of congruent triangles are congruent,
PR¯¯¯¯¯≅QR¯¯¯¯¯
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