![]() HL postulate(Hypotenuse – Leg OR RHS) -> If any two right angles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.Įxample : In ΔABC and ΔDEF are right angled triangle at B and E respectively.Angle Side Angle Postulate -> If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.Įxample : In ΔABC and ΔPQR,if ∠A =∠P AB = PQ and ∠B = ∠Q then Decide whether you can use the SSS or SAS Postulate to prove the triangles congruent.Angle Angle Side Postulate -> If two angles and a non-included side of a triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.Įxample : In ΔDEF and ΔXYZ,if ∠D =∠x, ∠E = ∠y and EF = YZ then.Side Side Side Postulate -> If the three sides of a triangle are congruent to the three sides of another triangle, then the two triangles are congruent.Įxample : In ΔABC and ΔPQR,if AB =PQ BC = QR and AC = PR then.(The included angle is the angle formed by the two sides.) The following figure illustrates this method. Side Angle Side Postulate -> If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.Įxample : In ΔMNO and ΔDEF,if MN =DE ∠N = ∠E and NO = EF then The SAS (Side-Angle-Side) postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.The following postulates and theorems are the most common methods for proving that triangles are congruent (or equal). ![]() ![]() ![]() To show that two triangles are congruent, it is not necessary to show that all six pairs of corresponding parts are equal. Two triangles are congruent if and only if there exists a correspondence between their vertices such that the corresponding sides and corresponding angles of two triangles are equal. Postulates of Congruent Triangle In this section we will discuss postulates of congruent triangles. The SAS Postulate states that if two sides and an included angle of one triangle are congruent to two sides and an included angle of a second triangle, then the. ![]()
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