CBSE Class 6 Mathematics Basic Geometrical Ideas Assignment Set 04

Question 1. Draw a rough diagram if possible of the following:
(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 minimum number of sides.
Answer:
(i) A circle or an oval is a closed curve that is not made up of line segments and hence is not a polygon.
(ii) A zigzag shape made of connected straight line segments that does not enclose an area.
(iii) Not possible. A polygon is a closed figure bounded by three or more line segments. A figure with only two sides cannot enclose a space.
(iv) A triangle, which has 3 sides.
In simple words: A polygon must have at least 3 straight sides to form a closed shape.

Exam Tip: Remember that polygons are strictly closed figures made of line segments. A figure with 2 sides cannot close.

Question 2. From the adjoining figure, answer the following:
(i) Is \(ABCDE\) a polygon?
(ii) Is \(O\) in the exterior of the polygon?
(iii) Is \(G\) in the interior of the polygon?
(iv) Is \(AC\) a diagonal of the polygon?
(v) How many diagonals this polygon has?
Answer:
(i) Yes, \(ABCDE\) is a 5-sided closed polygon (pentagon).
(ii) No, point \(O\) lies in the interior of the polygon.
(iii) No, point \(G\) lies in the exterior of the polygon.
(iv) Yes, \(AC\) connects two non-consecutive vertices and lies inside the polygon.
(v) 5 diagonals (\(AC\), \(AD\), \(BD\), \(BE\), \(CE\)).
In simple words: A diagonal connects non-adjacent corners inside a polygon.

Exam Tip: The number of diagonals in an \(n\)-sided polygon is given by the formula \(\frac{n(n-3)}{2}\).

Question 3. In this figure:
(i) How many rays?
(ii) Name opposite rays
(iii) Name two lines.
Answer:
(i) 6 rays (\(OC\), \(OB\), \(OA\), \(OF\), \(OE\), \(OD\)) starting from the common origin \(O$.
(ii) \(OB\) and \(OE\) (or \(OC\) and \(OF\), or \(OD\) and \(OA\)).
(iii) Line \(AD\) and Line \(CF$.
In simple words: A ray has one starting point and extends infinitely in one direction.

Exam Tip: Opposite rays share the same starting point and extend in exactly opposite directions along a straight line.

Question 4. If a point \(R\) is between points \(P\) and \(Q\), name pair of rays.
Answer:
The pair of rays are \(RP\) and \(RQ\) (or \(QP\) and \(PR\), etc.).
In simple words: When point \(R\) lies on the line segment \(PQ\), it creates rays pointing towards \(P\) and \(Q\).

Exam Tip: Always specify the starting endpoint first when naming a ray.

Question 5. Look at the figure and answer the following questions:
(i) Two adjacent sides
(ii) Three points on the polygon
(iii) One point in the interior
(iv) Two points in the exterior
(v) The polygon
Answer:
(i) \(AB\) and \(BC$
(ii) \(A\), \(B\), \(C$ (or any vertices on the boundary)
(iii) \(G$
(iv) \(I\), \(J$
(v) \(ABCDEF$
In simple words: Adjacent sides share a common vertex. Interior points are inside, exterior points are outside.

Exam Tip: Check whether points lie strictly on the boundary, inside, or outside the closed shape.

Question 6. In this figure, how many angles are there, name them.
Answer:
There are 6 angles.
\(\angle AOB\), \(\angle AOC\), \(\angle AOD\), \(\angle BOC\), \(\angle BOD\), \(\angle COD\).
In simple words: Count all individual angles and their combinations sharing the same vertex \(O\).

Answer:
(i) Nil (None)
(ii) \(C\), \(A\), \(D\), \(G$
(iii) \(E\), \(B\), \(O\), \(F$
In simple words: Points on the arms or vertex are "on" the angle. Points outside the opening are in the exterior.

Exam Tip: Pay close attention to whether a point lies directly on the ray lines forming the angle.

Question 8. Draw rough diagram of two line segments having:
(i) One common point
(ii) Two common point
(iii) Three common point
(iv) Four common point
Answer:
(i) Two intersecting line segments meeting at a single vertex point.
(ii) Not possible for straight line segments (two distinct straight lines can intersect at most at one point).
(iii) Not possible for straight line segments.
(iv) Not possible for straight line segments.
In simple words: Two straight line segments can only intersect at a maximum of one point unless they overlap completely.

Exam Tip: Straight lines or line segments cannot intersect at multiple points unless they are coincident (the exact same line segment).

Question 9. Does the vertex of an angle lie in its:
(i) Interior
(ii) Exterior
Answer:
(i) No
(ii) No
In simple words: The vertex is the endpoint/corner of the angle itself, so it lies on the angle, not strictly in its interior or exterior.

Exam Tip: The vertex is the joining point of the two rays forming the angle.

Question 10. How many angles does a polygon of:
(i) 5 sides
(ii) 10 sides
(iii) \(n\) sides has?
Answer:
(i) 5 angles
(ii) 10 angles
(iii) \(n\) angles
In simple words: An \(n\)-sided polygon always has exactly \(n\) vertices and \(n\) interior angles.

Exam Tip: Number of sides = Number of vertices = Number of interior angles in any polygon.