GSEB Class 6 Maths Solutions Chapter 14 પ્રાયોગિક ભૂમિતિ Exercise 14.3

Question 1. ભૂમિતિ રય્ નเ \( \overline{P Q} \) घे៧. \( \overline{P} \) દોરો. \( \overline{P Q} \)ને માપ્યા સિવાય, \( \overline{P Q} \)ની નકલની રચના કરો.
Answer:
1. First, draw a line segment \( \overline{PQ} \) whose *exact length* is *not known*.
2. Next, draw a line \( l \). *Then, mark* a point A on this line \( l \).
3. Place the *sharp point* of the compass on point P and *get* the measurement of \( \overline{P Q} \).
4. Now, *shift* the compass point to A and draw an arc on line \( l \) with the PQ measurement. *Identify* the point where this arc meets line \( l \) as B.
5. *As a result*, the segment AB on line \( l \) *now has* the same length as PQ.
In simple words: To make a copy of a line segment without measuring, first draw the original. Then, draw a long line and mark a starting point on it. Use a compass to pick up the length of the first segment and then transfer that exact length to the new line.

Exam Tip: To construct a copy of a line segment without measuring, always use a compass to transfer the exact length, ensuring accuracy in geometric constructions.

Question 2. કાઇ રખાખડ \( \overline{A B} \) આપેલો છે, જેની લંબાઈ તમે જાણતા નથી. જેની લંબાઈ \( \overline{A B} \) ની લંબાઈ કરતાં બમણી હોય તેવો રેખાખંડ \( \overline{P Q} \) રચો.
Answer:
1. We are *given* a line segment \( \overline{A B} \) whose *specific length* is unknown.
2. *After that*, draw a line \( l \). *Choose* a point P *anywhere* on this line.
3. Place the *needle* of the compass on point A and the pencil *tip* on point B. This *gives us* the length of \( \overline{A B} \).
4. Now, put the compass *needle* on point P and draw an arc on line \( l \). *Label* the point where the arc meets line \( l \) as C.
5. *Next*, *without changing* the compass measure, place its *needle* on point C and draw another arc to the right on line \( l \). Call the point where this arc *hits* line \( l \) as Q.
6. *Consequently*, \( \overline{P Q} \) is a line segment whose *overall length* is *exactly double* the length of \( \overline{A B} \).
7. This means *that* \( PQ = 2AB \).
In simple words: To make a line segment twice as long as another one: first, draw a long line and mark a starting point. Use your compass to measure the first segment. Then, mark that length on your new line, and from that new point, mark the same length again. This creates a segment that is double the original length.

Exam Tip: To double a line segment, first copy it once, then extend the compass from the new endpoint to copy it again, effectively adding the length twice.