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Write which of the following are true an...

Write which of the following are true and which are false?
(i) Every ray has a finite length.
(ii) Two lines intersect at a point. .
(iii) A terminated line can be produced indefinitely on both the sides.
(iv) A segment has one end point only.
(v) If two circles are equl, then their radii are equal.

Text Solution

AI Generated Solution

The correct Answer is:
Let's analyze each statement one by one to determine whether they are true or false. **(i) Every ray has a finite length.** A ray is defined as a part of a line that starts at a point and extends infinitely in one direction. Therefore, it does not have a finite length. **Conclusion:** False --- **(ii) Two lines intersect at a point.** Two lines can either intersect at a point, be parallel (and thus never intersect), or be coincident (overlapping completely). Therefore, it is not always true that two lines intersect at a point. **Conclusion:** False --- **(iii) A terminated line can be produced indefinitely on both sides.** A terminated line refers to a line segment that has two endpoints. However, according to Euclid's second postulate, a line can be extended indefinitely in both directions. Thus, a terminated line (line segment) itself cannot be produced indefinitely, but a line can be. **Conclusion:** True --- **(iv) A segment has one endpoint only.** A line segment is defined as a part of a line that has two endpoints. Therefore, stating that a segment has only one endpoint is incorrect. **Conclusion:** False --- **(v) If two circles are equal, then their radii are equal.** By definition, if two circles are equal, they have the same radius. Hence, if two circles are equal, their radii must also be equal. **Conclusion:** True --- ### Summary of Statements: 1. (i) False 2. (ii) False 3. (iii) True 4. (iv) False 5. (v) True ---
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