**Chapter 4 Basic Geometrical Ideas**

### Very Short Answer Type

Question 1.

Draw a rough sketch of:

(a) open curve

(b) closed curve

Solution:

Question 5.

Question 6.

In the given figure, name all the possible triangles.

Solution:

Possible triangles are:

(i) ∆ABC

(ii) ∆ABD

(iii) ∆ABE

(iv) ∆ACD

(a) ∆ACE

(vi) ∆ADE

Question 7.

Name all the angles in the given figure.

Solution:

In the given figure, the names of all the angles are:

(i) ∠ABC

(ii) ∠BCD

(iii) ∠CDA

(iv) ∠DAB

Question 8.

In the given figure, name all the line segments:

Solution:

In the given figure, the name of the line segments are:

### Short Answer Type

Question 9.

Using the given figure, name the following:

(a) Line containing point M.

(b) Line passing through four points.

(c) Line passing through three points.

(d) Two pairs of intersecting lines.

Solution:

Question 10.

Question 11.

How many lines can pass through

(i) one given point?

(ii) two given points?

(iii) three non-collinear points

Solution:

(i) Infinite number of lines can be passed through one given point.

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

(iii) Three lines can pass through three non- collinear points.

Question 12.

Look at the given figure and answer the following:

(a) Name the sides of the polygon ABCDEF.

(b) Name any two pairs of adjacent sides. .

(c) Name all the segments which intersect each other at one point.

(d) Name all the diagonals of the given polygon.

Solution:

Question 13.

Fill in the blanks.

(a) ……… is the largest chord of a circle.

(b) ……… divides the circle into two equal semi circles.

(c) Rectangle is a ……… curve.

(d) Triangle has ……… angles and three ……… .

(e) Only one line can be drawn through ……… points.

(f) ……… number of lines can pass through a given point.

(g) A closed figure made up of entirely of line segments is called a ……… .

(h) A curve which does not cross itself is called a ……… curve.

(i) The length of boundary of a circle is called its ……… .

Solution:

(a) Diameter

(b) Diameter

(c) Closed

(d) three, sides

(e) two

(f) Infinite

(g) polygon

(h) simple

(i) circumference

### Long Answer Type

Question 14.

### Multiple Choice Type

Question 15.

Least number of line segments required to make a polygon is

(a) 1

(b) 2

(c) 3

(c) 4

Solution:

Correct option is (c).

Question 16.

How many lines can be drawn through given two points?

(a) Only one

(b) 2

(c) 4

(d) Countless

Solution:

Correct option is (a).

Question 17.

How many vertices are there in a triangle?

(a) 1

(b) 2

(c) 3

(c) 4

Solution:

Correct option is (c).

Question 18.

Say ‘true’ or ‘False’.

(а) Two diameters of a circle will necessarily intersect.

(b) The centre of a circle always lies in the interior.

(c) The diameter is half of the radius of a circle.

(d) Longer chord is nearer to the centre of the circle.

Solution:

(a) True

(b) True

(c) False

(d) True

### Higher Order Thinking Skills (HOTS)

Question 19.

Draw an equilateral ∆ABC of any size. Draw AD as its median and an altitude AM.

(i) Does AD coincide with AM?

(ii) Name the point on the median which divides it in the ratio 1:2.

(iii) What is the measure of ∠ADC and ∠ADB?

(iv) Are D and M the same points?

Solution:

(i) Yes, AD coincides with AM.

(ii) The point on the median which divides it in the ratio 1 : 2 is called centroid of the triangle.

(iii) ∠ADC = ∠ADB = 90°

(iv) Yes, D and M are the same points.

Question 20.

In the given figure, l, m and n are three parallel lines, x andy intersect these lines.

(i) Name the points lying on the line x.

(ii) Name the points lying on the liney.

(iii) Name the points inside the quadrilateral ABED.

(iv) Name the points outside the quadrilaterals ABED and BCFE.

(v) Name the lines passing through three points.

Solution:

(i) A, B and C lie on the line x.

(ii) D, E and F lie on the liney.

(iii) Q is the point inside ▢ABED

(iv) Points R and S are outside the quadrilaterals ABED and BCFE.

(v) Lines x andy pass through the three points A, B, C and D, E, F respectively.