Question

in the adjoining figure, ABCD is a quadrilateral with diagonal AC and DB. If
AB = DC and angleBCD= angle CBA, show that
a) ∆BCD = ∆ABC
b) angleBCD = angle BAD
c) angleBCA = angleCBD​

Answer 1

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.

Hope it’s help You