This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Geometry – Constructing a Quadrilateral”.

1. 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 given

View Answer

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.

2. 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 constructed

View Answer

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.

3. One can construct a unique quadrilateral by the knowledge of any four quantities.

a) True

b) False

View Answer

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.

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) 4

View Answer

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. 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 sides

View Answer

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.

6. Which of the following is a valid quadrilateral?

a) ▀ABCD ∠A=60,∠B=120,∠C=120,∠D=90

b) ▀PQRS ∠A=90,∠B=90,∠C=90,∠D=90

c) ▀LMNO ∠A=90,∠B=150,∠C=90,∠D=60

d) ▀EFGH ∠A=120,∠B=120,∠C=120,∠D=120

View Answer

Explanation: The basic property of any quadrilateral is that the sum of all the internal angles is 360°. Here except ▀PQRS the sum of all the internal angles of other quadrilaterals is greater than 360°. Hence all the other quadrilateral other then ▀PQRS are incorrect.

7. Which of the following is an invalid quadrilateral?

a) ▀ABCD ∠A=60,∠B=120,∠C=120,∠D=90

b) ▀PQRS ∠A=90,∠B=90,∠C=90,∠D=90

c) ▀LMNO ∠A=90,∠B=150,∠C=60,∠D=60

d) ▀EFGH ∠A=100,∠B=20,∠C=120,∠D=120

View Answer

Explanation: The basic property of any quadrilateral is that the sum of all the internal angles is 360°. Here except ▀ABCD the sum of all the internal angles of other quadrilaterals is equal to 360°. Hence all the other quadrilaterals except ▀ABCD are incorrect.

**Sanfoundry Global Education & Learning Series – Mathematics – Class 8**.

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