Question

In quadrilateral abcd if diagonal ac bisects angle a and ab is equal to ad then show taht angle cbo is equla to angle cdo

Answer 1

Answer:

Step-by-step explanation:

Given that diagonal AC bisects angle A

=>∠DAO = ∠BAO

Also given that AB = AD

Now Consider triangles ABC and ADC, we have

AB = AD (given)

∠DAC = ∠BAC (given)

AC = AC (common side)

Henceby S-A-S axiom , both triangle are congruent,

=> BC = CD.-----(*)

Also ∠DCO = ∠BCO.-----(**)

Now consider triangle DOC and BOC,

DC = BC (from *)

∠DCO = ∠BCO (from **)

OC = OC (common side)

=> Both the triangles ODC and OBC are congruent as per S-A-S axiom

Hence, ∠CDO = ∠CBO ( Angles opposite to common side)