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Axioms are assumed
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.
Which of the following statements are true and which are false? Give reasons for your answers.
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