# Free Basic Geometrical Ideas Subjective Test 02 Practice Test - 6th grade

What is an angle? Mention all the elements of an angle.[1 MARK]

#### SOLUTION

Solution :

An angle is made up of two rays having a common endpoint.
The two rays forming the angle are called 'sides' or 'arms' of the angle, and the common endpoint is called the 'vertex' of the angle.

Navi said that railway lines are parallel, whereas Shashank said that railway lines are not parallel. Who is correct and why?
[2 MARKS]

#### SOLUTION

Solution :

Property: 1 Mark
Application: 1 Mark

According to the property of parallel lines, the distance between them is always constant.
Navi is correct because the distance between the railway lines is always constant. What are rays? Give some examples of rays that we observe daily. [2 MARKS]

#### SOLUTION

Solution :

Definition: 1 Mark
Example: 1 Mark

A ray is a portion of a line. It starts at one point (called starting point) and goes endlessly in a direction.
The various other rays which we observe are Sun rays, rays coming from the headlight of cars, etc. What is a quadrilateral? Explain with examples. [3 MARKS]

#### SOLUTION

Solution :

Definition: 1 Mark
Explanation: 1 Mark
Example: 1 Mark A quadrilateral is a type of polygon. It has four sides.
Quadrilateral means "four sides" (quad means four, lateral means side).

It is a 2-dimensional closed shape and has straight sides.

In the quadrilateral, ABCD, here (AB, BC), (BC, CD), (CD, DA) and (DA, AB) are the adjacent side whereas (AB, CD) and (AD, BC) are the opposite sides.
The four angles are ABC, BCD, CDA, DAB.

In the given figure find out the opposite angles and opposite sides. Also, name the diagonals for the given figure. [3 MARKS]

#### SOLUTION

Solution :

Angles: 1 Mark
Sides: 1 Mark
Diagonals: 1 Mark In the given figure the opposite angles are (∠DAB,∠BCD) & (∠ADC, ∠ABC).
The side DA is opposite to BC, and the side CD is opposite to AB.
AC and BD are the diagonals.

Draw figures with label according to the information given below.
(a)  AB and CD intersect at O.
(b)  Line m contains X and Y but not A.
(c)  TP and TS meet at T.
[3 MARKS]

#### SOLUTION

Solution : Figures: 1 Mark each

(a) (b) (c) What is the diameter, radius, and chord in a circle? Explain. Also, state the properties of chords of a circle. [4 MARKS]

#### SOLUTION

Solution :

Definition: 2 Marks
Properties: 2 Marks A radius is a line segment that connects the centre to a point on the circle.

The diameter is a straight line which starts at one point of the circle, goes through the centre and ends on the other point.

A chord of a circle is a straight line segment whose endpoints both lie on the circle.

Following are the properties of chords of a circle:

1. Chords are equidistant from the centre only if their lengths are equal.

2. A chord that passes through the centre of a circle is called a diameter, and it is the longest chord.

Name the points and then the line segments in each of the following figures. [4 MARKS]

#### SOLUTION

Solution :

Each option: 1 Mark

(i)  Points in figure (i) are A, B and C. The line segments are AB, BC, and AC.

(ii)   Points in figure (ii) are A, B, C and D. The line segments are AB, BC, CD and DA.

(iii)   Points in figure (iii) are A, B, C, D and E. The line segments are AB, BC, CD, DE and AE.

(iv)  Points in figure (iv) are A, B, C, D, E and F. The line segments are AB, CD and EF.

Answer the questions based on the following diagram. [4 MARKS] a) Identify three triangles in the figure.
b) Write the names of seven angles
c) Write the names of six line segments
d) Which two triangles have B as common?

#### SOLUTION

Solution : Each option: 1 Mark

a)  In the above figure, the three triangles are
ΔABC,ΔABD, and ΔADC.

b)  The seven angles are
ABCBACACBADBADCBADCAD

c)  The six line segments are:
¯AB,¯BD,¯DC,¯AC,¯BC,¯AD

d)  The triangles which have B as common are,
ΔABC and ΔABD.

Draw rough diagrams of two angles such that they have:-
a) One point in common
b)  Three points in common.
c) Four points in common
d) One ray in common
[4 MARKS]

#### SOLUTION

Solution : Each option: 1 Mark

a) b) c) d) 