RBSE Solutions Class 6 Maths Chapter 9 Simple Two Dimensional Shapes Exercise 9.1

Question 1. Classify the following curves as (A) Open or (B) Closed.
Answer:
(A) Open curves – (i), (vi)
(B) Closed curves – (ii), (iii), (v)
In simple words: An open curve has ends that do not meet, like a path you can walk along. A closed curve forms a complete loop, so you would end up where you started if you traced it.

🎯 Exam Tip: To check if a curve is open or closed, imagine drawing it without lifting your pencil. If you lift your pencil and the start and end points do not meet, it's open. If they meet, it's closed.

Question 2. Which all letters from A to Z are closed curves?
Answer: The closed curve from A to Z is 'O'. The letter 'O' forms a complete, unbroken loop, which is the definition of a closed curve.
In simple words: The letter 'O' is a closed curve because it makes a full circle with no openings.

🎯 Exam Tip: Remember that a closed curve must fully enclose a region without any gaps, like a circle or a square. Other letters might appear closed but have small openings.

Question 3.
(i) Which points lie in the interior part of the rectangle?
(ii) Which points lie in the exterior part of the rectangle?
(iii) Are N and L lie on the boundary of the rectangle?
Answer:
(i) The points P, Q, and R lie in the interior part of the rectangle. These points are completely inside the rectangle's shape.
(ii) The points S, U, and T lie in the exterior part of the rectangle. These points are completely outside the rectangle's shape.
(iii) Yes, the points N and L lie on the boundary of the rectangle. This means they are directly on the lines that form the rectangle's edges.
In simple words: Interior points are inside, exterior points are outside, and boundary points are on the edge of the shape.

🎯 Exam Tip: Clearly identify the region for interior, exterior, and boundary. Think of the boundary as the fence around a field; inside is the field, outside is everything else.

Question 4. Draw if possible, each one of the following with a rough diagram
(i) A closed curve that is not a polygon.
(ii) An open curve made up entirely of line segments.
(iii) A polygon with two sides.
(iv) A polygon with four sides.
Answer:
(i) A closed curve that is not a polygon: A circle is a good example. It is closed but made of a smooth curve, not straight line segments.
(ii) An open curve made up entirely of line segments: A zig-zag line or a V-shape. These are made of straight lines but do not connect to form a closed shape.
(iii) A polygon with two sides: This is impossible. A polygon needs at least three straight line segments to form a closed figure.
(iv) A polygon with four sides: A square or a rectangle is a perfect example. They are made of four straight line segments and are closed shapes.
In simple words: We can draw shapes that are closed but not polygons (like a circle) and open shapes made of straight lines. We cannot draw a polygon with only two sides because a polygon needs at least three sides to close. A square is a simple polygon with four sides.

🎯 Exam Tip: Remember the basic definitions: polygons must be closed shapes made only of straight line segments. A curve can be closed or open, and can be made of straight or curved lines.

Question 5. Adjust five points A, B, C, D and E in a figure of a polygon such that,
(i) Points A and C lie in the interior part of the polygon.
(ii) Points B and D lie in the exterior part of the polygon.
(iii) Point E lies on the boundary of the polygon.
Answer: To meet these conditions, we can draw a polygon, such as a pentagon. Place points A and C inside the shape. Place points B and D outside the shape. Lastly, place point E directly on one of the polygon's edges. For instance, if you draw a pentagon, place A and C inside, B and D outside, and E on one of its five sides. This placement correctly shows the interior, exterior, and boundary points for a polygon.
In simple words: Draw a polygon. Put points A and C inside it, B and D outside it, and E right on its edge.

🎯 Exam Tip: When drawing such diagrams, make sure the points are clearly distinguishable in their respective regions (inside, outside, or on the line) to avoid confusion.