Page 78 - Start Up Mathematics_6

Example 4: Draw a rough sketch of the following figures and label them:

(a) Point P on AB and Q outside AB (b) Two parallel lines PQ and RS
(c) XY intersecting PQ at M (d) OR and OS meeting at O

(e) Collinear points P, Q and R (f) Concurrent lines AB, CD and EF

X
Q Q
B
Solution: (a) P (b) P (c) M
Q S
A R P
Y
R E
A D
(d) (e) Q R (f) B
P C O
S F
O
Example 5: Consider the line QP shown in the given figure. State whether the following statements
are true or false in its context.

(a) Q, M, O, N, P are points on line MN. P
(b) Q and P are the points on line segment MN. N
(c) P lies on ray ON. O
(d) Ray OP is the same as ray OM. M
(e) There are ten line segments formed by points Q
Q, M, O, N and P.
(f) There are two rays in the given figure.
(g) Infinite number of lines are formed by Q, M, O, N and P.
Solution: (a) True (b) False (c) True (d) False (e) True (f) False (g) False

Open and Closed Figures
The figures having different beginning and end points are called open figures. However, the figures
having the same beginning and end points are called closed figures. Examples of open and closed
figures are as follows:

(i) (ii) (iii) (iv) (v) (vi)

Clearly, (i) and (ii) are open figures and the remaining figures are closed.

Simple Curves
A curve is a path drawn on a sheet of paper without lifting the pencil and without retracing any
part of the path except for single points. If a curve does not cross itself, then it is called a simple
curve. In the above figures, all the curves except (iv) are simple.

Interior and Exterior of Closed Figures

A closed curve divides the plane into three parts:
(i) The points lying inside the closed curve are called its interior.

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