Question

In figure, abc
.CD, AB-AC and BD=CD. By which rule, the triangles are congruent ?
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Answer 1

Answer:

. In quadrilateral ABCD we have

                  AC = AD

            and AB being the bisector of ∠A.

            Now, in ΔABC and ΔABD,

                  AC = AD

[Given]

                  AB = AB

[Common]

∠CAB = ∠DAB [∴ AB bisects ∠CAD]

            ∴ Using SAS criteria, we have

                  ΔABC ≌ ΔABD.

            ∴ Corresponding parts of congruent triangles (c.p.c.t) are equal.

            ∴ BC = BD.