Question

In figure given, if AC = BD, show that AB = CD. State the Euclid’s postulate/axiom used for the same.

Answer 1

Hint: Here, write AC as sum of AB and BC and BD as sum of BC and CD, then apply Euclid’s axiom of subtracting equal from equal and we get the same result.

Complete step-by-step answer:

Given, AC = BD …(i)
From the figure,
B is the point between A and C, therefore AC = AB + BC
Similarly, C is the point between B and D, therefore BD = BC + CD
On putting these values of AC and BD in equation (i), we get
 AB + BC = BC + CD …(ii)
According to Euclid’s axiom, when equals are subtracted from equals, remainders are also equal.
[Postulate is a statement that is assumed to be true or the base point for further definitions and arguments. Postulates are basic building materials. But postulates are not just meaning of mathematical terms like definitions]
Applying the above axiom, subtracting BC from both sides of equation (ii), we have
AB + BC – BC = BC + CD – BC
⇒ AB = CD [by using axiom 3 of Euclid]

Note: In this question use Euclid’s axiom to show the result. Do not directly show by drawing a figure; try to use the standard result and concepts which are already given. For these types of questions use the terms like postulates/Axioms etc.
Alternatively, by drawing a figure we can see that BC is common in AB and BD so if we remove line BC, we will simply get the result i.e., AB = CD.