Question

if AC =BD prove AB=CD​

Answer 1

Answer:

Here, we use

axiom 3 which states that equals are subtracted from equals  then the remainders are also equal.

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Solution:

 

Given, AC = BD......(1)

From the figure,

AC = AB + BC 

&

BD = BC + CD

 

On putting these values in eq 1,

⇒ AB +

BC = BC + CD

According to Euclid’s axiom, when equals are

subtracted from equals, remainders are also equal.

On Subtracting BC from  both sides,

AB + BC – BC = BC + CD – BC

AB = CD                 [ by axiom 3 of Euclid]

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Hope this will help you....