In the adjoining figure, ABCD is a quadrilateral with diagonal AC and

1.	In the adjoining figure, ABCD is a quadrilateral with diagonal AC and DB. IfAB = DC and angleBCD= angle CBA, show thata) ∆BCD = ∆ABCb) angleBCD = angle BADc) angleBCA = angleCBD
Answer» 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

In the adjoining figure, ABCD is a quadrilateral with diagonal AC and DB. IfAB = DC and angleBCD= angle CBA, show thata) ∆BCD = ∆ABCb) angleBCD = angle BADc) angleBCA = angleCBD

Answer»

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

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In the adjoining figure, ABCD is a quadrilateral with diagonal AC and DB. IfAB = DC and angleBCD= angle CBA, show thata) ∆BCD = ∆ABCb) angleBCD = angle BADc) angleBCA = angleCBD​

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In the adjoining figure, ABCD is a quadrilateral with diagonal AC and DB. IfAB = DC and angleBCD= angle CBA, show thata) ∆BCD = ∆ABCb) angleBCD = angle BADc) angleBCA = angleCBD