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1.	“For every line x and for every point o not lying on x, there exists a unique line y passing through o and parallel to x.” This statement is __________(a) Pythagoras’ theorem(b) Heron’s theorem(c) Thales’ theorem(d) Playfair’s axiomThe question was posed to me in examination.The origin of the question is Equivalent Versions of Euclid’s Fifth Postulate topic in division Euclid’s Geometry of Mathematics – Class 9
Answer» Right CHOICE is (d) Playfair’s axiom Best explanation: The given STATEMENT is Playfair’s axiom which is in fact, EQUIVALENT version of EUCLID’s FIFTH postulate. It can be understood by seeing the diagram given below. We can see that lines x and y are parallel, i.e. they will not intersect each other.

2.	When the sum of the measures of the interior angles on the same side of the falling line is greater than 180 degree, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is greater than 180 degree.(a) True(b) FalseThe question was posed to me in an interview for internship.I would like to ask this question from Equivalent Versions of Euclid’s Fifth Postulate topic in portion Euclid’s Geometry of Mathematics – Class 9
Answer» Right option is (b) False Best EXPLANATION: The given statement is slightly DIFFERENT from Euclid’s 5^th postulate which is “When the sum of the measures of the interior angles on the same side of the FALLING line is less than TWO right angles (<180), then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.” It can be understood by the diagram given below. Falling line is PQ and sum of two angles BPQ and YQP is greater than 180 degree and we can see that lines AB and XY will not meet on the right side of the line PQ.

3.	If P, Q and R are three points on a line and Q lies between P and R, then __________(a) PR + QR = PR(b) PQ + PR = PR(c) PQ + PR = QR(d) PQ + QR = PRThe question was asked in homework.The above asked question is from Euclid’s Axioms and Postulates topic in portion Euclid’s Geometry of Mathematics – Class 9
Answer» Correct ANSWER is (d) PQ + QR = PR The EXPLANATION: We can SEE in below diagram that Q is between P and R and hence PQ + QR = PR.

4.	How much lines can pass from two distinct points?(a) Zero(b) Only one(c) Only two(d) InfiniteI got this question in quiz.Query is from Euclid’s Axioms and Postulates in chapter Euclid’s Geometry of Mathematics – Class 9
Answer» The correct option is (b) Only one To explain I would say: According to Euclid’s axiom, given two distinct POINTS, there is a UNIQUE line that passes through them. As shown in below figure, there is only one line that can PASS through two distinct points O and P.

5.	How much lines can pass from one point?(a) One(b) Two(c) Infinite(d) ZeroI had been asked this question in homework.Asked question is from Euclid’s Axioms and Postulates topic in section Euclid’s Geometry of Mathematics – Class 9
Answer» Right CHOICE is (c) Infinite To explain I would say: As shown in below figure, we can DRAW as much lines as we want which are PASSING from one POINT O. Hence, infinite lines can pass from one point.

6.	Things which are equal to the same thing are equal to each other.(a) True(b) FalseI had been asked this question in a job interview.My question is from Euclid’s Axioms and Postulates in division Euclid’s Geometry of Mathematics – Class 9
Answer» Correct option is (a) True The best explanation: Above STATEMENT is one of the Euclid’s axioms. It can be understood by the FOLLOWING example: Let a = b and a = c, then we can SIMPLY state that b = c. Here, b and c are EQUAL to same THING (a here) so they are equal to each other.

7.	How many dimensions does a line have?(a) Zero(b) One(c) Two(d) ThreeThis question was posed to me in an internship interview.My question comes from Euclid’s Geometry Definitions in portion Euclid’s Geometry of Mathematics – Class 9
Answer» CORRECT option is (b) One Easy explanation: ACCORDING to EUCLID’s definition, a line is BREATHLESS length. Hence, a line has only one dimension, i.e. Length.

8.	How many dimensions does a point have?(a) One(b) Two(c) Three(d) ZeroThis question was posed to me in homework.I want to ask this question from Euclid’s Geometry Definitions in chapter Euclid’s Geometry of Mathematics – Class 9
Answer» Correct choice is (d) Zero To EXPLAIN I would SAY: According to EUCLID’s DEFINITION, a point doesn’t have length, breadth and height. Therefore a point has zero DIMENSION.

9.	What does geometry mean?(a) Measurement of land(b) Measurement of physical objects(c) Measurement of velocity(d) Measurement of PressureI have been asked this question in a national level competition.Origin of the question is Euclid’s Geometry Definitions topic in portion Euclid’s Geometry of Mathematics – Class 9
Answer» Right ANSWER is (a) Measurement of land Explanation: The word geometry comes from the Greek WORDS geo which means the earth and metrein which means to MEASURE. THEREFORE geometry is assumed to have ORIGINATED from the need for measuring land.