Special Cases of Construction Quiz - CBSE Class 8 Mathematics

Free practice quiz: Special Cases of Construction (CBSE Class 8 Mathematics). 10 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

Sample questions

1. Construct a triangle with sides 4cm, 6cm, and 8cm. Which special case of triangle construction does this represent?

   1. Equilateral triangle
   2. Isosceles triangle
   3. Scalene triangle
   4. Right-angled triangle
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   Answer: C. Scalene triangle

   A scalene triangle has all three sides of different lengths. Since the given sides (4cm, 6cm, 8cm) are all different, it's a scalene triangle.

2. Construct an isosceles triangle with sides 5cm and 5cm and a base angle of 60°. What type of special triangle is also created?

   1. Scalene triangle
   2. Equilateral triangle
   3. Right-angled triangle
   4. Obtuse-angled triangle
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   Answer: B. Equilateral triangle

   Since the two sides are equal and the base angle is 60°, the other base angle will also be 60° (due to isosceles triangle properties). The sum of angles in a triangle is 180°, so the third angle is also 60°. Thus, all angles are 60° forming an equilateral triangle.

3. You are given only the base and the corresponding altitude of a triangle. Is it possible to construct the triangle uniquely? If not, how many such triangles can be constructed?

   1. Yes, only one triangle
   2. No, infinitely many triangles
   3. No, two triangles
   4. No, three triangles
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   Answer: B. No, infinitely many triangles

   With only the base and altitude, the third vertex can lie anywhere on a line parallel to the base at a distance equal to the altitude. This allows for infinite possibilities for the triangle's shape.

4. Explain why constructing a triangle with angles 60°, 70°, and 60° results in an isosceles triangle.

   1. Because all angles are acute
   2. Because two angles are equal
   3. Because the sum of angles is 190°
   4. Because it's an equilateral triangle
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   Answer: B. Because two angles are equal

   An isosceles triangle is defined as having at least two equal angles. The given angles have two 60° angles, making it an isosceles triangle. Note that it is also an equilateral triangle, but the question asks specifically for the property making it isosceles.

5. Construct a triangle with sides 5cm, 5cm and 6cm. What type of triangle is formed?

   1. Right-angled triangle
   2. Isosceles triangle
   3. Equilateral triangle
   4. Scalene Triangle
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   Answer: B. Isosceles triangle

   An isosceles triangle has at least two sides equal. Since two sides are 5cm each, it's an isosceles triangle.

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