Question

In the given figure,
OA=OB
OC=OD
/_ AOB= /_ COD
(/_ means angle)

Prove that AC=BD​

Answer 1

Step-by-step explanation:

Given ∠AOB=∠COD

∠AOB−∠COB=∠COD−∠COB

∴∠AOC=∠DOB

In ΔAOC and ΔDOB

i)OA=OB(Given)

ii)OC=∠OD (Given)

iii)∠AOC=∠DOB (Proved above)

∴ΔAOC≅∠DOB

(SAS Axiom)

∴AC=BD

Answer 2

Answer:

○GIVEN-

OA=OB

OC=OD

Angle AOB=Angle COD

○TO PROVE-

AC=BD

○PROOF-

Let :-

Angle AOC be 1

Angle COB be 2

Angle BOD be 3

Angle AOB be 4

Angle COD be 5

Angle AOB=Angle AOC+ Angle COB

=>4=1+2 - [1]

Angle COD=Angle BOD+ Angle COB

=>5=2+3 - [2]

Angle AOB=Angle COD [GIVEN]

=>4=5

=>1+2=2+3 [From 1 and 2]

[Canceling 2 from both the sides ]

=>1=3

=>Angle AOC =Angle BOD - [3]

OA=OB [Given]

OC=OD [Given]

Angle AOC =Angle BOD [From 3]

Therefore,

Triangle AOC is congruent to triangle BOD by SAS congruency criterion

Therefore,

AC=BD by CPCT

HENCE, PROOVED