ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 10 Basic Geometrical Concept Ex 10.3
Question 1.
Draw rough diagrams to illustrate the following:
(i) open simple curve
(ii) closed simple curve
(iii) open curve that is not simple
(iv) closed curve that is not simple.
Solution:
(i) open simple curve
(ii) closed simple curve
(iii) open curve that is not simple
(iv) closed curve that is not simple
Question 2.
Consider the given figure and answer the following questions:
(i) Is it a curve?
(ii) Is it a closed curve?
(iii) Is it a polygon?
Solution:
(i) Yes, it is a curve.
(ii) Yes, it is a closed curve.
(iii) Yes, it is a polygon.
Question 3.
Draw a rough sketch of a triangle ABC. Mark a point P in its interior and a point Q in its exterior. Is the point A in its exterior or in its interior?
Solution:
The point A is neither in the exterior nor in the interior of triangle ABC. It is on the triangle ABC.
Question 4.
Draw a rough sketch of a quadrilateral PQRS. Draw its diagonals. Name them.
Solution:
The meeting point O of the diagonals PR and QS of the quadrilateral PQRS is in the interior of the quadrilateral PQRS.
Question 5.
In context of the given figure:
(i) Is it a simple closed curve?
(ii) Is it a quadrilateral?
(iii) Draw its diagonals and name them.
(iv) State which diagonal lies in the interior and which diagonal lies in the exterior of the quadrilateral.
Solution:
(i) Yes
(ii) Yes.
(iii) Its diagonals are \(\overline{\mathrm{AC}}\) and \(\overline{\mathrm{BD}}\).
(iv) Diagonal \(\overline{\mathrm{AC}}\) is in the interior and diagonal \(\overline{\mathrm{BD}}\) is in the exterior of quadrilateral ABCD.
Question 6.
Draw a rough sketch of a quadrilateral KLMN. State,
(i) two pairs of opposite sides
(ii) two pairs of opposite angles
(iii) two pairs of adjacent sides
(iv) two pairs of adjacent angles.
Solution:
(i) \(\overline{\mathrm{KL}}, \overline{\mathrm{NM}} \text { and } \overline{\mathrm{KN}}, \overline{\mathrm{ML}}\)
(ii) ∠K, ∠M and ∠N, ∠L
(iii) \(\overline{\mathrm{KL}}, \overline{\mathrm{KN}} \text { and } \overline{\mathrm{MM}}, \overline{\mathrm{ML}} \text { or } \overline{\mathrm{KL}}, \overline{\mathrm{LM}}\) and \(\overline{\mathrm{NM}}, \overline{\mathrm{ML}}\)
(iv) \(\angle \mathrm{K}, \angle \mathrm{L} \text { and } \angle \mathrm{M}, \angle \mathrm{N} \text { or } \angle \mathrm{K}, \angle \mathrm{L} \text { and } \angle \mathrm{L}\), \(\angle \mathrm{M}\) etc.