Question

In fig. AC = XD, C is the mid-point of AB and D is the mid-point of XY. Using a Euclid's axiom, show that AB = XY.

Assertion: According to Euclid's 1st axiom- "Things which are equal to the same thing are also equal to one another". Reason: If AB = PQ and PQ = XY, then AB = XY.

In a Mathematics class, the teacher taught a chapter "Introduction to Euclid's Geometry" from the NCERT Mathematics book. The next day, the teacher showed a picture of a mathematician and asked the following questions to the students about the mathematician's contributions to the field of mathematics.

If A, B and C are three points on a line, and B lies between A and C, then prove that AB + BC = AC.