__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**

**Answer:**

(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.*

**Answer**

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

*Question 3*

*Answer according to the figure*

** **

*(a) Line passing through A.*

*(b) Line containing point D.*

*(c) Two pairs of intersecting lines.*

*(d) Line on which X lies.*

**Answer **

(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?*

**Answer**

(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.*

* ***Answer**

(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 \(\vec{PQ}\).*

**Answer**

(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.**

**Answer**

(a) Open

(b)Closed

(c)Open

(d)Closed

(e)Closed

*Question 2*

*Draw diagrams according to the given instructions*

*(a) Closed (b)Open*

**Answer**

(a)

(b)

*Question 3*

*Draw a polygon and color its interior part.*

**Answer**

*Question 4*

*Is the given figure curve and closed?*

**Answer**

Yes, it is curve

Yes, it is closed.

**Exercise 4.3**

*Question 1*

*Give the name of the angles in the given figure*

**Answer**

\(\angle CDA\), \(\angle DAB\), \(\angle ABC\), \(\angle BCD\)

*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 \(\angle ROT\)*

**Answer**

(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*

**Answer**

(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?*

**Answer:**

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?*

**Answer:**

Point L lies on the interior of the triangle.

All solutions are not given

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