Question

OA = OB, OC = OD, ANGLE AOB=ANGLE COD. Prove that AC = BD

Answer 1

in triangle AOD and triangle COD

OA=OB ( given)
OC=OD (given)
angleAOB=angle COD (given )
so triangle AOD and triangle COD correspond to triangle by side angle side

so AC=BD BY CPCT

Answer 2

Answer:

Given : angle AOB = angle COD ------ (1)

and angle COB = angle COB -----(2)

same angles

so if we subtract equation 2 in equation 1 we get : angle AOB - angle COB = angle COD - angle COB

we know " Euclid 's third axiom if equals be subtracted from equals the remainder are equals we get

angle AOC = angle BOD -------(3)

in triangle AOC and triangle BOD

OA = OB ( given )

angle AOC = angle BOD ( from equation 3)

and OC = OD ( given )

thus,

triangle AOC congruent triangle BOD ( by SAS rule )

therefore,

AC = BD ( by C.P.C.T )

hence proved