CBSE Class 8 Mathematics Congruence of Triangles MCQs Set 15

Mathematics Objective Questions and Answers: Congruence of Triangles

Access targeted multiple-choice questions for Congruence of Triangles designed to align with the latest CBSE academic syllabus for Class 8 Mathematics. These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.

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Multiple Choice Questions

Question 1: An exterior angle of a triangle is 110° and one of the interior opposite angles is 30°. Find the other two angles of the triangle.
(a) 80° and 70°
(b) 80° and 75°
(c) 85° and 75°
(d) 85° and 70°
Show Answer & Explanation

Answer: (a) 80° and 70°

Explanation:
1. Exterior angle = sum of the two interior opposite angles, so the other opposite angle = 110° − 30° = 80°.
2. The third angle (adjacent to the exterior angle) = 180° − 110° = 70°.

Teacher's Note:
1. Use the exterior angle property.
2. Check: 30° + 80° + 70° = 180°.

Question 2: Which of the following is NOT correct?
(a) Sides opposite to equal angles of a triangle may be unequal
(b) The bisectors of two equal angles of a triangle are equal
(c) Angles opposite to equal sides of a triangle are equal
(d) The measure of each angle of an equilateral triangle is 60°
Show Answer & Explanation

Answer: (a) Sides opposite to equal angles of a triangle may be unequal

Explanation:
1. Sides opposite to equal angles are always equal (converse of the isosceles triangle theorem).
2. The other three statements are true.

Teacher's Note:
1. Recall the isosceles triangle theorem and its converse.
2. Identify the false statement.

Question 3: AD, BE and CF, the altitudes of triangle ABC, are equal. Then triangle ABC is
(a) a right isosceles triangle
(b) an isosceles triangle only
(c) an equilateral triangle
(d) a scalene triangle
Show Answer & Explanation

Answer: (c) an equilateral triangle

Explanation:
1. Area = ½ × BC × AD = ½ × CA × BE = ½ × AB × CF; with equal altitudes, BC = CA = AB.
2. So the triangle is equilateral.

Teacher's Note:
1. Equal altitudes imply equal bases.
2. Use the area formula with each base.

Question 4: In a triangle ABC, D, E and F are the mid-points of BC, CA and AB. If AB = 7 cm, BC = 8 cm and CA = 9 cm, the perimeter of triangle DEF is
(a) 28 cm
(b) 12 cm
(c) 14 cm
(d) 24 cm
Show Answer & Explanation

Answer: (b) 12 cm

Explanation:
1. By the mid-point theorem EF = BC/2, DE = AB/2, DF = CA/2.
2. Perimeter of DEF = (7 + 8 + 9) / 2 = 12 cm.

Teacher's Note:
1. The medial triangle has half the perimeter.
2. Apply the mid-point theorem to each side.

Question 5: In a triangle, P, Q and R are the mid-points of sides BC, CA and AB respectively. If AC = 21 cm, BC = 29 cm and AB = 30 cm, the perimeter of the quadrilateral ARPQ is
(a) 51 cm
(b) 53 cm
(c) 55 cm
(d) 57 cm
Show Answer & Explanation

Answer: (a) 51 cm

Explanation:
1. AR = AB/2 = 15 cm and AQ = AC/2 = 10.5 cm.
2. RP = AC/2 = 10.5 cm and PQ = AB/2 = 15 cm.
3. Perimeter = 15 + 10.5 + 15 + 10.5 = 51 cm.

Teacher's Note:
1. ARPQ is a parallelogram.
2. Opposite sides equal: 2 × (15 + 10.5) = 51.

Question 6: Of the three angles of a triangle, one is twice the smallest and another is three times the smallest. The smallest angle is
(a) 60°
(b) 90°
(c) 30°
(d) 45°
Show Answer & Explanation

Answer: (c) 30°

Explanation:
1. x + 2x + 3x = 180°, so 6x = 180° and x = 30°.
2. The angles are 30°, 60°, 90°.

Teacher's Note:
1. Use the angle sum property.
2. Express all angles in terms of the smallest.

Question 7: In triangle ABC, 2∠A = 3∠B = 6∠C. Then ∠C is
(a) 45°
(b) 55°
(c) 30°
(d) 60°
Show Answer & Explanation

Answer: (c) 30°

Explanation:
1. Let 2∠A = 3∠B = 6∠C = k: ∠A = k/2, ∠B = k/3, ∠C = k/6.
2. k/2 + k/3 + k/6 = k = 180°, so ∠C = 30°.

Teacher's Note:
1. Introduce a common value k.
2. k/2 + k/3 + k/6 = k.

Question 8: If two sides of a triangle are unequal, then the larger side has the ___ angle opposite to it.
(a) right
(b) larger
(c) smaller
(d) equal
Show Answer & Explanation

Answer: (b) larger

Explanation:
1. In a triangle the greater side is opposite the greater angle.

Teacher's Note:
1. Longer side faces the larger angle.
2. Converse: larger angle faces the longer side.

Question 9: The sum of any two sides of a triangle is ___ the third side.
(a) equal to
(b) half of
(c) greater than
(d) less than
Show Answer & Explanation

Answer: (c) greater than

Explanation:
1. By the triangle inequality, the sum of any two sides exceeds the third side.

Teacher's Note:
1. Needed for three lengths to form a triangle.
2. Difference of two sides is less than the third.

Question 10: In a right triangle the hypotenuse is the ___ side.
(a) shortest
(b) middle
(c) longest
(d) equal to the base
Show Answer & Explanation

Answer: (c) longest

Explanation:
1. The hypotenuse is opposite the right angle, the largest angle, so it is the longest side.

Teacher's Note:
1. Greatest angle faces the longest side.
2. By Pythagoras, c² = a² + b² exceeds a² and b².

Question 11: If two angles of a triangle are unequal, then the smaller angle has the ___ side opposite to it.
(a) longer
(b) shorter
(c) equal
(d) parallel
Show Answer & Explanation

Answer: (b) shorter

Explanation:
1. The smaller angle is opposite the shorter side.

Teacher's Note:
1. Side opposite the smaller angle is shorter.
2. Angle and side order are the same.

Question 12: The difference of any two sides of a triangle is ___ the third side.
(a) double
(b) greater than
(c) less than
(d) equal to
Show Answer & Explanation

Answer: (c) less than

Explanation:
1. From the triangle inequality a < b + c we get a − b < c.

Teacher's Note:
1. Triangle inequality in another form.
2. Difference of two sides is less than the third.

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