Proof of SAS Congruency Test of two triangles

SAS Test math blogTheorem: If two triangles have two sides of the one equal to two sides of the other, each to each, and the angles included by those sides equal, then the triangles are equal in all respects.

Construction: Let ABC, DEF be two triangles in which AB=DE and

AC=DF and the included angle \angle BAC is equal to included angle \angle EDF.

It is required to prove that the

\Delta ABC = \Delta DEF in all respects.

Proof: Apply the \Delta ABC to the \Delta DEF so that the point A falls on the point D; and the side AB along the side DE. Then, because AB=DE so the point B must coincide with the point E. And, because AB falls along DE, and the

\angle BAC=\angle EDF, so AC must fall along DF. And, because

AC=DF, the point C must coincide with the point F. Then, since B coincides with E, and C with F, hence, the side BC must coincide with the side EF. Hence, the \Delta ABC coincides with the \Delta DEF, and is therefore equal to it in all respects. QED.

More later…please post your questions, comments, and I will gladly answer them asap

Nalin Pithwa

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