Question

From the given figure, prove that (i) BD = AC (ii) DO = CO

Answer 1

Proved that BD=AC using SAS congruency ,  and  shown DO = CO

Step 1:

From the given figure

AD ≅ BC

∠BAD ≅ ∠ABC  

AB ≅ AB  ( common side)

Using SAS congruence

ΔBAD ≅ ΔABC

Step 2:

Corresponding parts of congruent triangles are congruent

Hence

BD = AC   ( QED)

∠ABD = ∠BAC

Step 3:

∠ABD  = ∠ABO

∠BAC = ∠BAO

in ΔAOB  , Sides opposite to Equal angles are equal Hence

AO = BO

Step 4:

BD = AC  

BD = BO + DO

AC = AO + CO

=> BO + DO = AO + CO

AO = BO already shown above

Hence DO = CO

QED

Proved that BD=AC using SAS congruency ,  and  shown DO = CO

(Your Question missing figure but that has been attached)