**Exercise – 4.1**

**1. Use the figure to name :**

(1) Five points

(2) Aline

(3) Four rays

(4) Five line segments

**Solution:** (1) Five points : O, B, C, D, E

(2) A line: DB

(3) Four rays.: OD, OE,OC, OB

(4) Five line segments: DE, OE, OC, OB, OD

**2. Name the line given in all possible (twelve) ways, choosing only two letters at a time from the four given.**

**Solution:** Possible lines are AB, AC, AD, BC, BD,CD, BA, CA, DA, CB, DB, DC

**3. Use the figure to name:**

(1) Line containing point E.

(2) Line passing through A.

(3) Line on which O lies

(4) Two pairs of intersecting lines.

**Solution:** (1) A line containing point £ is AE.

(2) A line passing through A is AE.

(3) A line on which O lies is CO or OC

(4) Two pairs of intersecting lines are AD, CO and AE, FE

**4. How many lines can pass through (1) one given point? (2) two given points?**

**Solution:** (1) Infinite number of lines can pass through one given point.

(2) Only one line can pass through two given points.

**5. Draw a rough figure and label suitably in each of the following cases:**

(1) Point Plies on AB.

(2) XY and PQ intersect at M.

(3) Line/ contains E and F but not D.

(4) OP and OQ meet at O.

(1).

(2).

(3).

(4).

**6. Consider the following figure of line IVIN. Say whether following statements are true or false in context of the given figure.**

(1) Q, M, 0, N, P are points on the line MN.

(2) M, 0, N are points on a line segment MN.

(3) M and N are end points of line segment MN.

(4) O and N are end points of line segment OP.

(5) M is one of the end points of line segment QO.

(6) M is point on ray OP-

(7) Ray OP is different from ray QP.

(8) Ray OP is same as ray OM.

(9) Ray OM is not opposite to ray OP.

(10) 0 is not an initial point of OP.

(11) N is the initial point of NP and NM

**Solution:** (1) True

(2) True

(3) True

(4) False

(5) False

(6) False

(7) True

(8) False

(9) False

(10) False

(11) True

**Exercise – 4.2 **

1. Classify the following curves as (2) Open or (3) Closed

**Solution:** (1) Open curve

(2) Closed curve

(3) Open curve

(4) Closed curve

(5) Closed curve

**2. Draw rough diagrams to illustrate the following :**

(1) Open curve

(2) Closed curve.

**Solution:** (1) Open curves :

(2) Closed curves :

**3. Draw any polygon and shade its interior.**

**Solution:**

ABCDEF is the required polygon.

**4. Consider the given figure and answer the questions :**

(1) Is it a curve?

(2) Is it closed?

**Solution:** (1) Yes, it is a curve.

(2) Yes, it is closed.

**5. Illustrate, if possible, each one of the following with a rough diagram:**

(1) A closed curve that is not a polygon.

(2) An open curve made up entirely of line segments.

(3) A polygon with two sides.

**Solution:**

(1)

(2)

(3) Polygon with two sides cannot be drawn.

**Exercise – 4.3**

**1. Name the angles in the given figure.**

**Solution:** There are four angles in the given figure i.e, ∠ABC, ∠CDA, ∠DAB, ∠DCB

**2. In the given diagram, name the point(s)**

(1) In the interior of ∠DOE

(2) In the exterior of ∠EOF

(3) On /EOF

**Solution:** (1) Point in the interior of ∠DOE : A

(2) Points in the exterior of ∠EOF :C, A, D

(3) Points on ∠EOF : E, O, B, F

**3. Draw rough diagrams of two angles such that they have**

(1) One point in common.

(2) Two points in common.

(3) Three points in common.

(4) Four points in common.

(5) One ray in common.

**Solution:** (1)

Here, two angles are AOd and BOC and point O is common.

(2)

Here, two angles are ∠AOB and ∠CDE and two points F and G are common.

(3)

Here, two angles are ∠AOB and ∠CDE and three points F, D and G are common.

(4)

Here, two angles are ∠AOB and ∠CDE and four points F, G, H and I are common.

(5)

Here, two angles are ∠AOB and ∠AOC and ray OA is common.