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1.	Which of the following is an invalid quadrilateral?(a) &uhblk;ABCD ∠A=60,∠B=120,∠C=120,∠D=90(b) &uhblk;PQRS ∠A=90,∠B=90,∠C=90,∠D=90(c) &uhblk;LMNO ∠A=90,∠B=150,∠C=60,∠D=60(d) &uhblk;EFGH ∠A=100,∠B=20,∠C=120,∠D=120This question was addressed to me in an online quiz.The query is from Geometry topic in section Practical Geometry of Mathematics – Class 8
Answer» The correct choice is (a) &uhblk;ABCD ∠A=60,∠B=120,∠C=120,∠D=90 Best explanation: The BASIC PROPERTY of any quadrilateral is that the sum of all the INTERNAL ANGLES is 360°. Here except &uhblk;ABCD the sum of all the internal angles of other quadrilaterals is equal to 360°. Hence all the other quadrilaterals except &uhblk;ABCD are INCORRECT.

2.	Which of the following is a valid quadrilateral?(a) &uhblk;ABCD ∠A=60,∠B=120,∠C=120,∠D=90(b) &uhblk;PQRS ∠A=90,∠B=90,∠C=90,∠D=90(c) &uhblk;LMNO ∠A=90,∠B=150,∠C=90,∠D=60(d) &uhblk;EFGH ∠A=120,∠B=120,∠C=120,∠D=120The question was posed to me in my homework.The origin of the question is Geometry topic in chapter Practical Geometry of Mathematics – Class 8
Answer» Right choice is (b) &uhblk;PQRS ∠A=90,∠B=90,∠C=90,∠D=90 For explanation I would say: The BASIC property of any QUADRILATERAL is that the sum of all the internal angles is 360°. Here except &uhblk;PQRS the sum of all the internal angles of other quadrilaterals is GREATER than 360°. HENCE all the other quadrilateral other then &uhblk;PQRS are incorrect.

3.	What would be the general formula of number of details to be known, for constructing a quadrilateral?(a) (n-1)… where n is the number of sides(b) (n+1)… where n is the number of sides(c) (n×2)… where n is the number of sides(d) (n/2)… where n is the number of sidesThis question was posed to me at a job interview.I would like to ask this question from Geometry topic in division Practical Geometry of Mathematics – Class 8
Answer» RIGHT choice is (b) (n+1)… where n is the NUMBER of sides The best explanation: If ONE WISHES to construct a unique quadrilateral, the requirement is (n+1) number of details. If any student has n number of details, the CONSTRUCTED quadrilateral would not be a unique quadrilateral.

4.	If one desires to construct a unique triangle (i.e. three sided polygon), how many details are required?(a) 1(b) 2(c) 3(d) 4I got this question in a national level competition.My doubt is from Geometry topic in chapter Practical Geometry of Mathematics – Class 8
Answer» Right answer is (d) 4 For EXPLANATION: The basic condition to construct any triangle is having at least FOUR INFORMATION about the triangle, one cannot construct a unique triangle without that. So, the options other than 4 would be INCORRECT. Hence 4 is the correct answer.

5.	One can construct a unique quadrilateral by the knowledge of any four quantities.(a) True(b) FalseThe question was posed to me during an interview.The query is from Geometry in chapter Practical Geometry of Mathematics – Class 8
Answer» Right answer is (b) False For EXPLANATION: The basic CONDITION for constructing a quadrilateral is, knowing five or more details about the POLYGON. So, here the statement would not be CORRECT for constructing a UNIQUE quadrilateral.

6.	A quadrilateral can be constructed _______ if the lengths of its four sides and a diagonal is given.(a) uniquely(b) complete(c) incomplete(d) can’t be constructedI have been asked this question during a job interview.The doubt is from Geometry in section Practical Geometry of Mathematics – Class 8
Answer» The correct OPTION is (a) uniquely The best explanation: If we want to CONSTRUCT quadrilateral we need at least FIVE information about the quadrilateral. If we have four sides and a diagonal then we can construct a UNIQUE quadrilateral.

7.	Which of the following conditions does not fulfill the condition for constructing a quadrilateral?(a) When four sides and one diagonal are given(b) When two diagonals and three sides are given(c) When two adjacent sides and three angles are given(d) When two adjacent sides and two angles are givenThe question was asked in a national level competition.My doubt is from Geometry topic in section Practical Geometry of Mathematics – Class 8
Answer» The CORRECT choice is (d) When two adjacent SIDES and two angles are given The best explanation: If we want to construct quadrilateral we need at least five information about the quadrilateral, but the ANSWER states that two adjacent sides and two angles here we have only four information. So here we cannot construct a quadrilateral.