Question

In ABC and ABD, if DA = CB and  DAB =  CBA, prove that AOB is isosceles.

Answer 1

GIVEN,

AD = BC

∠1 = ∠2

∠3 = ∠4

TO PROVE : BD = AC

PROOF :

HERE,

IN Δ A0D AND Δ BOC

AD = BC (GIVEN)

∠1 = ∠2 (GIVEN)

∠AOD = ∠BOC (VERTICALLY OPP. ANGLES)

∴ Δ A0D ≅ Δ BOC (BY AAS)

SO, OD = OC (CPCT)--------------------------------------1

NOW,

IN Δ AOB

∠3 =∠4

OB = OA (ISOSCELES Δ PROP.)-----------------------------2

THEN,

OD + OB = OC + OA (ADDING 1 AND 2)

∴ BD = AC

HENCE PROVED

Answer 2

Step-by-step explanation:

GIVEN,

AD = BC

∠1 = ∠2

∠3 = ∠4

TO PROVE : BD = AC

PROOF :

HERE,

IN Δ A0D AND Δ BOC

AD = BC (GIVEN)

∠1 = ∠2 (GIVEN)

∠AOD = ∠BOC (VERTICALLY OPP. ANGLES)

∴ Δ A0D ≅ Δ BOC (BY AAS)

SO, OD = OC (CPCT)--------------------------------------1

NOW,

IN Δ AOB

∠3 =∠4

OB = OA (ISOSCELES Δ PROP.)-----------------------------2

THEN,

OD + OB = OC + OA (ADDING 1 AND 2)

∴ BD = AC

HENCE PROVED

this the right answer

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