Congruence Axiom
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Side-Angle-Side (SAS) Congruence Axiom Theorem: Two triangles are congruent if any two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle. Given: Two triangle, Triangle ABC and Triangle DEF such that AB=DE, AC=DF and ∠A = ∠D
To Prove: Triangle ABC ≅ Triangle DEF
Proof: Place Triangle ABC on Triangle DEF such that side AB falls on side DE with vertex A on vertex D and vertex B on vertex E. Since ∠A = ∠D , therefore AC will fall on DF. As AC=DF, therefore, C will fall on F.
Thus AB coincides with DE and AC coincides with DF. Now, B falls on E and C falls on F. Therefore, BC coincides with EF. Thus Triangle ABC on being superposed on Triangle DEF , covers it exactly. Hence Triangle ABC ≅ Triangle DEF (By definition of congruence).
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To Prove: Triangle ABC ≅ Triangle DEF
Proof: Place Triangle ABC on Triangle DEF such that side AB falls on side DE with vertex A on vertex D and vertex B on vertex E. Since ∠A = ∠D , therefore AC will fall on DF. As AC=DF, therefore, C will fall on F.
Thus AB coincides with DE and AC coincides with DF. Now, B falls on E and C falls on F. Therefore, BC coincides with EF. Thus Triangle ABC on being superposed on Triangle DEF , covers it exactly. Hence Triangle ABC ≅ Triangle DEF (By definition of congruence).
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