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Introduction to Congruent Triangles, Congruent Figures, Congruent figures are exactly equal in size and shape., , Congruent Triangles, If all the sides and angles of a triangle are equal to the corresponding sides and angles of, another triangle, then both the triangles are said to be congruent., , Here, △ABC, , ≅ △DEF, , Criteria for Congruency, SSS Criteria for Congruency, If under a given correspondence, the three sides of one triangle are equal to the three, corresponding sides of another triangle, then the triangles are congruent., , SAS Criteria for Congruency, If under a correspondence, two sides and the angle included between them of a triangle, are equal to two corresponding sides and the angle included between them of another, triangle, then the triangles are congruent.

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ASA Criteria for Congruency, If under a correspondence, two angles and the included side of a triangle are equal to two, corresponding angles and the included side of another triangle, then the triangles are, congruent., , AAS Criteria for Congruency, AAS Rule: Triangles are congruent if two pairs of corresponding angles and a pair of opposite, sides are equal in both triangles., , Why SSA and AAA congruency rules are not valid?, Two triangles with equal corresponding angles need not be congruent. In such a, correspondence, one of them can be an enlarged copy of the other. Therefore AAA, congruency is not valid.

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If two triangles have two congruent sides and a congruent non included angle, then, triangles are not necessarily congruent. Therefore, SSA congruency is not valid., , RHS Criteria for Congruency, If under a correspondence, the hypotenuse and one side of a right-angled triangle are, respectively equal to the hypotenuse and one side of another right-angled triangle, then, the triangles are congruent., , Criteria for Congruency, Criteria for Congruency of two triangles are:, (i) SSS Rule, (ii) SAS Rule, (iii) ASA Rule, (iv) RHS Rule