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State T for true and F for false. (i) ...

State T for true and F for false.
(i) It is possible to divide a line segment in 5 equal parts by perpendicularly bisecting a given line segment 5 times.
(ii) With a given centre and a given radius, only one centre be drawn.
(iii) If we bisect an angle of a square, then we get two angles of `45^@` each

A

`{:(i" "ii" "iii),(F" "T" "T):}`

B

`{:(i" "ii" "iii),(F" "T" "F):}`

C

`{:(i" "ii" "iii),(T" "F" "T):}`

D

`{:(i" "ii" "iii),(T" "T" "F):}`

Text Solution

AI Generated Solution

The correct Answer is:
**Step-by-Step Solution:** 1. **Statement (i):** "It is possible to divide a line segment in 5 equal parts by perpendicularly bisecting a given line segment 5 times." - To analyze this statement, we consider the process of perpendicular bisecting a line segment. Each time we bisect a line segment, we divide it into two equal parts. - If we perform this operation 5 times, we will create 2^5 = 32 segments. However, these segments will not be equal to 5 equal parts; rather, they will be 32 segments in total, which means that the statement is false. - **Conclusion:** This statement is **False (F)**. 2. **Statement (ii):** "With a given centre and a given radius, only one circle can be drawn." - A circle is defined by its center and radius. If we have a specific center point and a specific radius, there can only be one unique circle that can be drawn with those parameters. - Any attempt to draw another circle with the same center and radius will overlap with the first, confirming that only one circle can exist under these conditions. - **Conclusion:** This statement is **True (T)**. 3. **Statement (iii):** "If we bisect an angle of a square, then we get two angles of 45 degrees each." - A square has four right angles, each measuring 90 degrees. When we bisect one of these angles, we divide it into two equal parts. - Therefore, each part will measure 90 degrees / 2 = 45 degrees. This confirms that the statement is correct. - **Conclusion:** This statement is **True (T)**. **Final Answers:** (i) F (ii) T (iii) T ---
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