GSEB Class 6 Maths Solutions Chapter 4 ભૂમિતિના પાયાના ખ્યાલો Exercise 4.2

Question 1. નીચેના વક્રનું (i) ખુલ્લા અને (ii) બંધ વક્રમાં વર્ગીકરણ કરો:
Answer: A curve is called a closed curve if its ends are connected. Conversely, a curve is called an open curve if its ends are not joined together. Based on these definitions, in the given figures, (a) and (c) represent open curves. On the other hand, figures (b), (d), and (e) are closed curves.

In simple words: Closed curves have their ends joined up, making a complete shape. Open curves have ends that do not meet, so they are not fully enclosed.

Exam Tip: Remember that a closed curve always forms a boundary for an area, while an open curve does not.

Question 2. નીચેની પરિસ્થિતિ દર્શાવતી રફ આકૃતિ દોરોઃ
(a) ખુલ્લો વક્ર
(b) બંધ વક્ર
Answer:
(a) The curve shown below is an open curve because its ends do not connect with each other.
(b) The curve shown below is a closed curve because its ends join together to form a complete boundary.
In simple words: An open curve doesn't connect at the ends, like a letter 'C'. A closed curve connects at both ends, like a circle or a square.

Exam Tip: When drawing a rough figure, make sure it clearly shows the defining characteristic of either an open or a closed curve.

Question 3. કોઈ પણ બહુકોણ દોરી તેનો અંદરનો ભાગ છાયાંકિત કરો.
Answer: Here, PQRS is a polygon. The internal area of polygon PQRS has been shaded.
In simple words: You need to draw a shape with straight sides (a polygon), like a square or triangle, and then color inside it.

Exam Tip: Polygons are always closed figures made entirely of straight line segments. Remember to shade the *interior* only.

Question 4. નીચે આપેલી આકૃતિ પરથી પ્રશ્નોના જવાબ આપોઃ
(a) શું તે વક્ર છે?
(b) શું તે બંધ છે?
Answer:
(a) Yes, it is a curve. Every polygon is a type of curve, and this figure is composed of straight line segments.
(b) Yes, it is a closed curve. This is because all its endpoints are joined, forming a completely enclosed shape.
In simple words: The shape is made of lines and is a curve. It is also closed because all its lines meet up to form a full loop.

Exam Tip: A curve is a broad term; a polygon is a specific type of curve made of straight line segments. Always check if the figure's ends meet to decide if it's closed.

Question 5. જો શક્ય હોય, તો નીચેની પરિસ્થિતિ દર્શાવતી રફ આકૃતિ દોરોઃ
(a) બંધ વક્ર કે જે બહુકોણ ન હોય.
(b) ખુલ્લો વક્ર કે જે સંપૂર્ણપણે રેખાખંડનો બનેલો હોય.
(c) બે બાજુવાળો બહુકોણ
Answer:
(a) The figure shown here is a closed curve, but it is not a polygon. Observe that in this figure, one side is curved rather than being a line segment. Polygons, by definition, are closed figures constructed solely from straight line segments.
(b) The figure shown below is an open curve. This curve is made entirely of straight line segments. The two ends of the figure do not connect with each other, thus making it an open curve.
(c) It is not possible to draw a polygon with only two sides. Polygons must have at least three straight line segments to form a closed shape.
In simple words: For (a), draw a shape that closes but has at least one curved side, like an egg. For (b), draw a zig-zag line or a shape like a 'W' using only straight lines, but leave the ends open. For (c), you cannot draw a polygon with just two sides because it won't close up.

Exam Tip: Understand the strict definitions: polygons require at least three straight sides and must be closed. A curve can be open or closed, and can have straight or curved parts.