Constructing Quadrilaterals Quiz - CBSE Class 8 Mathematics

Free practice quiz: Constructing Quadrilaterals (CBSE Class 8 Mathematics). 11 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

Sample questions

1. Which of the following is NOT sufficient information to construct a quadrilateral?

   1. Four sides and one diagonal
   2. Three sides and two diagonals
   3. Two adjacent sides and three angles
   4. Three angles and two included sides
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   Answer: B. Three sides and two diagonals

   While you can construct a triangle with three sides, a quadrilateral needs more information than just three sides. Two diagonals provide extra information than necessary, leading to ambiguity.

2. You are given three angles of a quadrilateral as 70°, 80°, and 100°. What is the measure of the fourth angle?

   1. 50°
   2. 110°
   3. 100°
   4. Cannot be determined
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   Answer: B. 110°

   The sum of angles in a quadrilateral is 360°. Therefore, 360° - (70° + 80° + 100°) = 110°

3. Construct a kite with diagonals of length 10cm and 6cm. What is the area of the kite?

   1. 30cm²
   2. 60cm²
   3. 120cm²
   4. Cannot be determined
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   Answer: A. 30cm²

   Area of a kite is half the product of the diagonals (1/2 * 10cm * 6cm = 30cm²).

4. What's the minimum information required to uniquely construct a cyclic quadrilateral?

   1. Four sides
   2. Four angles
   3. Three sides and one angle
   4. Two sides and two angles
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   Answer: A. Four sides

   Given four sides of a cyclic quadrilateral, you can use Ptolemy's Theorem to find the lengths of the diagonals and then construct the quadrilateral.

5. Under what conditions is it impossible to construct a quadrilateral given the lengths of its four sides?

   1. When the sum of lengths of any three sides is greater than the fourth side
   2. When the sum of lengths of any three sides is less than the fourth side
   3. When the sides form a rectangle
   4. When the quadrilateral is cyclic
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   Answer: B. When the sum of lengths of any three sides is less than the fourth side

   This violates the triangle inequality theorem, making construction impossible.

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