Bihar School Examination Board (BSEB) Class 8 Mathematics: Practical Geometry

Instructions. Answer all questions. Fill exactly one bubble per question on the OMR sheet.

1. Practical Geometry

   1.

   Which of the following conditions is NOT sufficient to construct a unique quadrilateral?

   1. (A)

      Three sides and two diagonals

   2. (B)

      Two adjacent sides and three angles

   3. (C)

      Three sides and two included angles

   4. (D)

      Four sides and one diagonal

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   Answer: (A)

   Three sides and two diagonals

   To construct a unique quadrilateral, we need specific measurements. Three sides and two diagonals do not always guarantee a unique quadrilateral; for example, the order of sides relative to diagonals can vary, leading to different quadrilaterals.

   Practical Geometry · Medium

2. 2.

   To construct a square, what is the minimum information required?

   1. (A)

      Length of one diagonal

   2. (B)

      Area of the square

   3. (C)

      Perimeter of the square

   4. (D)

      Length of one side

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   Answer: (D)

   Length of one side

   A square has all sides equal and all angles 90 degrees. Knowing the length of one side is sufficient as all other properties can be derived from it.

   Practical Geometry · Easy

3. 3.

   Which tool is primarily used for drawing arcs and circles in geometric constructions?

   1. (A)

      Ruler

   2. (B)

      Set square

   3. (C)

      Compass

   4. (D)

      Protractor

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   Answer: (C)

   Compass

   A compass is specifically designed for drawing circles and arcs of a given radius.

   Practical Geometry · Easy

4. 4.

   When constructing a quadrilateral given four sides and one diagonal, how many triangles are effectively formed?

   1. (A)

      Three

   2. (B)

      One

   3. (C)

      Four

   4. (D)

      Two

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   Answer: (D)

   Two

   A diagonal divides a quadrilateral into two triangles. Therefore, constructing two triangles using the given side lengths and diagonal is the basis for constructing the quadrilateral.

   Practical Geometry · Medium

5. 5.

   To construct a parallelogram, what is the minimum information needed?

   1. (A)

      Lengths of two diagonals

   2. (B)

      Lengths of one side and two angles

   3. (C)

      Lengths of two adjacent sides and one angle

   4. (D)

      Lengths of all four sides

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   Answer: (C)

   Lengths of two adjacent sides and one angle

   For a parallelogram, knowing two adjacent sides and the included angle is sufficient because opposite sides are equal and parallel, and opposite angles are equal.

   Practical Geometry · Hard

— End of the paper · updated 14 October 2026 —