Question

Let AB and CD be two line segments such that AD and BC intersect at O. Suppose AO = OC and BO = OD. Prove that AB = CD.

Answer 1

Given : AB and CD two line segments

such that AD and BC intersect at O.

AO = OC

BO = OD

To prove : AB = CD

proof :

In ∆AOB and ∆COD

AO = OC ( Given )

<AOB = <COD ( vertically opposite angles )

BO = OD ( Given )

Therefore ,

∆AOB ≅ ∆COD

[ SAS congruence rule ]

AB = CD [ C.P.CT ]

••••

Answer 2

Hey there!

Step-by-step explanation:

Given,

AB and CD are line segments.

AO = OC

and BO = OD

To prove : AB = CD.

Proof:

Statement                      (Reason)

in ΔAOB and ΔCOD,

AO = OC                         (given)

BO = OD                          (given)

∠AOB = ∠COD               (vertically opp. ∠s)

ΔAOB ≅ ΔCOD               ( By SAS axiom)

AB = CD                            (cpctc)

Hope It Helps You!