Question 1: Which of the following statements are true and which are false? Give reasons for your answers.
- Only one line can pass through a single point.
- There are infinite numbers of lines which pass through two distinct points.
- A terminated line can be produced indefinitely on both the sides.
- If two circles are equal, then their radii are equal.
- In the following figure, if AB = PQ and PQ = XY, than AB = XY.
Answer: (1) False. As we know that there are various points in a plane. Such that A, B, C, D AND E. Now by first postulate we know that a line may be drawn from a given point to another point.
So, we can draw a line from A to B, A to C, A to D, and A to E. It proves that many lines can pass through point A.
Hence, we conclude that infinite lines can pass through a single point.
Answer: (2) False.
Let us mark two points A and B on the plane of paper. Now we fold the paper so that a crease passes through A. Since we know that an unlimited number of lines can pass through a point. So an unlimited number of lines can pass through A.
Again we fold the paper so that a line passes through B. Clearly infinite number of lines can pass through B. Now we fold the paper in such a way that a line passes through both A and B.
We observe that there is just only one line passing through both A and B.
Answer: (3) True, In geometry, by a line, we mean the line in its totality and not a portion of it. A physical example of a perfect line is not possible. Since a line extends indefinitely in both the directions.
So, it cannot be drawn or shown whole on paper. In practice, only a portion of a line is drawn and arrowheads are marked at its two ends indicating that it extends indefinitely in both directions.
Answer: (4) True, on super imposing the region bounded by one circle on the other if the circle coincides. Then, their centres and boundaries coincide. Therefore, their radii will be equal.
Answer: (5) True, because things which are equal to the same thing, are equal to one another.