Introduction to EUCLID'S GEOMETRY

Euclid’s second axiom (as per order given in the Textbook for Class IX) is

• The things which are equal to the same thing are equal to one another.

• If equals be added to equals, the wholes are equal.

• If equals be subtracted from equals, the remainders are equals.

• Things which coincide with one another are equal to one another.

Euclid’s fifth postulate is

• The whole is greater than the part.

• A circle may be described with any centre and any radius

• All right angles are equal to one another.

• If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines if produced indefinitely, meet on that side on which the sum of angles is less than two

  right angles.

The things which are double of the same thing are

• equal

• unequal

• halves of the same thing

• double of the same thing

Axioms are assumed

• theorems

• definitions

• universal truths specific to geometry

• universal truths in all branches of mathematics

John is of the same age as Mohan. Ram is also of the same age

as Mohan. State the Euclid’s axiom that illustrates the relative ages of John and Ram.

• fourth

• second

• first

• third

If a straight line falling on two straight lines makes the interior

angles on the same side of it, whose sum is 120°, then the two straight lines, if produced

indefinitely, meet on the side on which the sum of angles is

• less than 120°

• greater than 120°

• is equal to 120°

• greater than 180°

‘Lines are parallel if they do not intersect’ is stated in the form of

• an axiom

• a definition

• a postulate

• a proof

The number of dimensions, a surface has :

• 1

• 2

• 3

• 0

The total number of propositions in the Elements are :

• 465

• 460

• 13

• 55

In Indus Valley Civilisation (about 3000 B.C.), the bricks used for construction work were having dimensions in the ratio

• 1 : 3 : 4

• 4 : 2 : 1

• 4 : 4 : 1

• 4 : 3 : 2