Question

Que:In the given figure, if AC = BD, then prove that AB = CD.

Answer 1

Answer:

Solution:

It is given, AC = BD

From the given figure, we get,

• AC = AB + BC
• BD = BC + CD

⇒ AB + BC = BC + CD [Given: AC=BD]

We know that, according to Euclid’s axiom, when equals are subtracted from equals, remainders are also equal.

Subtracting BC from the L.H.S and R.H.S of the equation AB + BC = BC + CD, we get,

AB + BC – BC = BC + CD – BC

AB = CD

Hence Proved !

Hope it will be helpful :)

Answer 2

Answer:

AC = AB + BC BD = BC + CD

It is given that AC = BD

AB + BC = BC + CD (1)

According to Euclid’s axiom, when equals are subtracted from equals, the remainders are also equal. Subtracting BC from equation (1), we obtain A B + BC − BC = BC + CD − BC A B = CD