Question 1. What is the Euclid’s second axiom?
Solution: The 2nd axiom is: “If equals be added to equals, the wholes are equal.”
Question 2. What is a theorem?
Solution: A mathematical statement whose truth has been logically established is called a theorem.
Question 3. What is the Euclid’s fifth postulate?
Solution: It states that: “If a straight line falling on two straight lines make 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 the side on which the sum of the angles is less than two right angles.”
Question 4. Is the following statement correct? “The axioms are Universal truths in all branches of Mathematics.”
Question 5. Complete the following statement: The things which are double of the same thing are ....................... .
Solution: The things which are double of the same thing are equal.
Question 6. In how many chapters Euclid divided his famous treatise, “The Elements”?
Solution: 13 Chapters.
Question 7. J, M and R are friends, J is of the same age as M. R is also of the same age as M.
Which Euclid’s axiom illustrates the relative age of J and R?
Solution: First Axiom.
Question 8. If a straight line falling on two straight lines makes the interior angles on the same side of it, whose sum is 120°, then on which side the two straight lines meet, if produced indefinitely?
Solution: They meet on the side on which the sum of angles is less than 120°.
Question 9. How many dimensions does a solid has?
Solution: A solid has 3 dimensions.
Question 10. How many dimensions does a surface has?
Solution: A surface has 2 dimensions.
Question 11. How many dimensions does a point has?
Solution: A point has zero (0) dimensions.
Question 12. Which of the following are the boundaries of a surface: lines; curves; surfaces?
Solution: The boundaries of a surface are curves.
Question 13. Johan is of the same age as Mohan. Raghu is also of the same age as Mohan. State Euclid’s axiom that illustrate the relative ages of Johan and Raghu.
Solution: The first axiom explains the above statement.
Question 14. Which of the following is the 5th postulate of Euclid?
(i) The whole is greater than the part.
(ii) If a straight line falling on two straight lines make 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.
(iii)“all right angles are equal to one another.”
Solution: The option (ii) is the Euclid’s fifth postulate.
Question 15. Which of the following are assumed as axioms?
(i) Universal Truths in all branches of Mathematics.
(ii) Universal Truths specific to geometry.
Solution: (i) The universal truths in all branches of Mathematics.
Question 16. Complete the following statement: Pythagoras was a student of ................................... .
Solution: Pythagoras was the student of ‘Thales’.
Question 17. What do we call a closed figure formed by three line segments
Solution: A triangle.
Question 18. What do we call a figure formed by two straight lines having a common point?
Solution: An angle.
Question 19. What is the minumum number of lines required to make a closed figure?
Solution: Three lines.
Question 20. How many straight lines can be drawn through two given points
Solution: Only one line.