# Chapter 4: Basic Geometrical Ideas

Exercise 4.1

Question 1:

Answer according to the figure given below

(a)  A line

(b) Four rays

(c)  Five points

(d) Five line segments

(a)  $$\overleftrightarrow{CE}$$

(b)  $$\overrightarrow{AC}$$, $$\overrightarrow{AB}$$, $$\overrightarrow{AD}$$, $$\overrightarrow{AE}$$

(c)   Five points are A, B, C, D and E.

(d)  $$\bar{ED}$$,$$\bar{DA}$$, $$\bar{AC}$$, $$\bar{AB}$$, $$\bar{CD}$$

Question 2

Name all the possible (twelve) lines choosing only two letters at a time from the figure given below.

$$\overleftrightarrow{PQ}$$, $$\overleftrightarrow{QR}$$, $$\overleftrightarrow{RS}$$, $$\overleftrightarrow{QP}$$, $$\overleftrightarrow{RQ}$$, $$\overleftrightarrow{SR}$$, $$\overleftrightarrow{PS}$$, $$\overleftrightarrow{SP}$$, $$\overleftrightarrow{PR}$$, $$\overleftrightarrow{RP}$$, $$\overleftrightarrow{QS}$$, $$\overleftrightarrow{SQ}$$

Question 3

(a)  Line passing through A.

(b)  Line containing point D.

(c)  Two pairs of intersecting lines.

(d)  Line on which X lies.

(a)  $$\overleftrightarrow{AD}$$

(b)  $$\overleftrightarrow{AD}$$

(c)  $$\overleftrightarrow{AD}$$ and $$\overleftrightarrow{XY}$$, $$\overleftrightarrow{AD}$$ and $$\overleftrightarrow{ED}$$.

(d)  $$\overleftrightarrow{XY}$$

Question 4

How many lines can pass through (i) one point (ii) two points?

(i)    There are infinite lines which can pass through one point.

(ii)    There is only one line which can pass through two given points.

Question 5

Draw figures with label according to the information given below

(a)  Point X lies on$$\bar{YZ}$$.

(b)  $$\overleftrightarrow{AB}$$ and $$\overleftrightarrow{CD}$$ intersect at O.

(c)  Line m contains X and Y but not A.

(d)  $$\overleftrightarrow{TP}$$ and $$\overleftrightarrow{TS}$$ meet at T.

(a)

(b)

(c)

(d)

Question 6

Consider the figure given below and answer whether the following statements are true or false.

(a)  T, Q, O, P, S are points lying on the line $$\overleftrightarrow{QP}$$.

(b)  Q, O and P are points on $$\bar{QP}$$.

(c)  Q and P are end points of $$\bar{QP}$$.

(d)  O and P are end points on $$\bar{OS}$$.

(e)  Q is one of the end points of $$\bar{TO}$$.

(f)  Q is point on $$\vec{OS}$$.

(g)  Ray OS is different from $$\vec{TS}$$.

(h)  Ray OS is same as $$\vec{OQ}$$.

(i)   Ray OQ is not opposite to $$\vec{OS}$$.

(j)   O is not an initial point of $$\vec{OS}$$.

(k)  P is the initial point of $$\vec{PS}$$ and $$\vec{PQ}$$.

(a)  True

(b)  True

(c)  True

(d)  False

(e)  False

(f)  False

(g)  True

(h)  False

(i)   False

(j)   False

(k)  True

Exercise 4.2

Question 1

Answer whether the following figures are closed or open.

(a)  Open

(b)Closed

(c)Open

(d)Closed

(e)Closed

Question 2

Draw diagrams according to the given instructions

(a)  Closed  (b)Open

(a)

(b)

Question 3

Draw a polygon and color its interior part.

Question 4

Is the given figure curve and closed?

Yes, it is curve

Yes, it is closed.

Exercise 4.3

Question 1

Give the name of the angles in the given figure

$$\angle CDA$$, $$\angle DAB$$, $$\angle ABC$$, $$\angle BCD$$

Question 2

Name the point(s) in the figure given below

(a)  Interior angle of$$\angle POS$$

(b)Exterior angle of $$\angle ROT$$

(c)On $$\angle ROT$$

(a)Q

(b)U, Q, P

(c)R, S, T, O

Question 3

Draw diagrams having two angles such that they have

(a)One point common

(b)Two points common

(c)Three points common

(d)Four points common

(e)One ray common

(a)

$$\angle QOS$$ and $$\angle POR$$ have O common point.

(b)

$$\angle ZOY$$ and $$\angle YOX$$ have O and Y common points.

(c)

$$\angle YOX$$ and $$\angle YOZ$$ have Y, W and O common points.

(d)

$$\angle COP$$ and $$\angle COQ$$ have C, B, A and O common points.

(e)

Ray $$\vec{OR}$$ is common between $$\angle QOR$$ and $$\angle POR$$.

Exercise 4.4

Question 1:

Draw a sketch of triangle PQR. Mark a point A interior and a point B in its exterior. Is the point Q is in its interior or in its exterior?

Point Q lies on the $$\Delta PQR$$ .

Question 2:

Draw a sketch of triangle XYZ. Mark a point L interior and a point M in its exterior. Is the point L is in its interior or in its exterior?

Point L lies on the interior of the triangle.