if AC = BD, then prove that AB = CD

6. In Fig. 5.10, if AC = BD, then prove that AB = CD.

From the above figure  we get that

AC     = AB + BC

BD     = BC + CD

It is given that AC = BD

Plug the value of AC we get

AB + BC      = BC + CD            … (1)

According to Euclid’s axiom,when equals are subtracted from equals, the remainders

are also equal.

Subtracting BC from both side in equation (1), we get

AB + BC − BC       = BC + CD − BC

AB     = CD

Hence proved