Question

Identify the statement(s) that are both biconditional and false. A. Three points are not in the same plane if and only if exactly one line passes through them. B. Exactly one line passes through three points if the points are in an infinite number of planes. C. An infinite number of planes pass through the same three points if and only if the points are not on the same line. D. Three points are on the same line if and only if exactly one plane passes through them.

Answer 1

Answer:

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Answer 2

Question :-

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

(ii) There are an infinite number of lines which pass through two distinct points.

answers.

(1) Only one line can pass through a single point.

(ii) A terminated line can be produced indefinitely on both the sides.

(iv) Iftwo circles are equal, then their radii are equal.

In Fig. 2.9. if AB=PQ and PQ=XY, then AB=XY.

​

Answer :-

(i) False

Reason : If we mark a point O on the surface of a paper. Using pencil and scale, we can draw infinite number of straight lines passing

through O.

(ii) False

Reason : In the following figure, there are many straight lines passing through P. There are many lines, passing through Q. But there is one and only one line which is passing through P as well as Q.

(iii) True

Reason: The postulate 2 says that “A terminated line can be produced indefinitely.”

(iv) True

Reason : Superimposing the region of one circle on the other, we find them coinciding. So, their centres and boundaries coincide.

Thus, their radii will coincide or equal.

(v) True

Reason : According to Euclid’s axiom, things which are equal to the same thing are equal to one another.

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