Question

Prove using diagram In the given figure, if AC = BD, then prove that AB = CD.
A B C D

Answer 1

Given,

AC=BD ... (i)

AC=AB+BC ……(ii) (Point B lies between A and C)

BD=BC+CD … (iii) (Point C lies between B and D)

Now,

substituting (ii) and (iii) in (i), we get

⇒AB+BC=BC+CD

⇒AB+BC–BC=CD

⇒AB=CD

Hence, AB=CD.