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19 August, 2011

Introduction to Euclid's Geometry- Brainstorming

Statement 1 Only one line can pass through a single point.

This statement is false. This is because passing through a single point; infinite number of lines can be drawn. Observe the following figure. Through the point L, many lines are passing.



Statement 2 There are an infinite number of lines which pass through two distinct points.

This statement is false. This is because through two distinct points, only one line can pass.

Try it!

Statement 3 A terminated line can be produced indefinitely on both the sides.

This statement is true. A terminated line can be produced indefinitely on both the sides.

Statement 4 If two circles are equal, then their radii are equal.This statement is true. Observe that in two equal circles, their centres as well as the outer boundary will coincide.

Statement 5 If AB = PQ and PQ = XY, then AB = XY.

This statement is true. Euclid’s first axiom states that things which are equal to the same thing are equal to one another. Therefore, the lines AB and XY will be equal to each other.

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