Here are the MCQs for Chapter 6 (Triangles) of Class 10 Maths, tailored for students preparing for their board exams. These questions, complete with answers, are designed based on the most recent exam format. They align with the latest CBSE syllabus 2024- 2025 and the NCERT curriculum. Presented with clear explanations, these multiple-choice questions help students effectively understand triangles and improve their scores. Additionally, you can find MCQs for other chapters in the Class 10 Maths curriculum.
MCQs for Class 10 Maths Chapter 6 Triangles – Question with Answers
Question: In a right-angled triangle, the square of the hypotenuse is equal to:
a) Sum of the squares of the other two sides
b) Difference of the squares of the other two sides
c) Twice the product of the other two sides
d) None of the above
Answer: a) Sum of the squares of the other two sides
Question: Two triangles are similar if their:
a) Corresponding angles are equal
b) Corresponding sides are equal
c) Corresponding sides are proportional
d) Both a and c
Answer: d) Both a and c
Question: In △ABC, if AB/DE = BC/EF = CA/FD, then △ABC is:
a) Congruent to △DEF
b) Similar to △DEF
c) Not related to △DEF
d) None of the above
Answer: b) Similar to △DEF
Question: If △PQR ~ △XYZ and PQ/XY = 2/3, then area of △PQR / area of △XYZ is:
a) 4/9
b) 9/4
c) 2/3
d) 3/2
Answer: a) 4/9
Question: In △ABC, AD is the median. If △ABD ~ △ACD, then △ABC is:
a) Right-angled triangle
b) Equilateral triangle
c) Isosceles triangle
d) None of the above
Answer: c) Isosceles triangle
Question: In △ABC, if AB² + BC² = AC², then the angle opposite to AC is:
a) 30°
b) 45°
c) 60°
d) 90°
Answer: d) 90°
Question: In a triangle, if two sides are 7 cm and 24 cm and the hypotenuse is 25 cm, the triangle is:
a) Right-angled triangle
b) Acute-angled triangle
c) Obtuse-angled triangle
d) None of the above
Answer: a) Right-angled triangle
Question: In △ABC, if AB = 6 cm, BC = 8 cm, and AC = 10 cm, then △ABC is:
a) Right-angled triangle
b) Equilateral triangle
c) Isosceles triangle
d) Scalene triangle
Answer: a) Right-angled triangle
Question: If △ABC ~ △DEF and AB = 3 cm, DE = 4 cm, BC = 6 cm, then EF is:
a) 8 cm
b) 6 cm
c) 4.5 cm
d) 5 cm
Answer: a) 8 cm
Question: In △PQR, if PQ² + QR² > PR², then the triangle is:
a) Right-angled
b) Acute-angled
c) Obtuse-angled
d) None of the above
Answer: b) Acute-angled
Question: In △ABC, if AB = AC, then △ABC is:
a) Scalene
b) Isosceles
c) Equilateral
d) None of the above
Answer: b) Isosceles
Question: If two triangles are similar, then their corresponding sides are:
a) Equal
b) Proportional
c) Unequal
d) None of the above
Answer: b) Proportional
Question: If △PQR ~ △XYZ and ∠P = 50°, ∠Q = 60°, then ∠Y is:
a) 50°
b) 60°
c) 70°
d) 80°
Answer: c) 70°
Question: If △ABC ~ △DEF and area of △ABC = 16 cm², area of △DEF = 64 cm², then (AB/DE)² is:
a) 1/4
b) 1/2
c) 1/16
d) 1/8
Answer: a) 1/4
Question: The ratio of the areas of two similar triangles is equal to the:
a) Ratio of their corresponding heights
b) Ratio of their corresponding medians
c) Ratio of the squares of their corresponding sides
d) Ratio of the cubes of their corresponding sides
Answer: c) Ratio of the squares of their corresponding sides
Question: In a right-angled triangle, the altitude to the hypotenuse is:
a) Smaller than both legs
b) Equal to one of the legs
c) Greater than both legs
d) The geometric mean of the segments into which the hypotenuse is divided
Answer: d) The geometric mean of the segments into which the hypotenuse is divided
Question: In △ABC, if AD is the angle bisector of ∠A, then AB/AC = BD/DC is known as:
a) Basic Proportionality Theorem
b) Angle Bisector Theorem
c) Pythagoras Theorem
d) None of the above
Answer: b) Angle Bisector Theorem
Question: If △ABC ~ △PQR and AB/QR = BC/PR, then which of the following is true?
a) ∠A = ∠P
b) ∠B = ∠Q
c) ∠C = ∠R
d) All of the above
Answer: d) All of the above
Question: In △ABC, if ∠B = 90°, AB = 5 cm, BC = 12 cm, then AC is:
a) 13 cm
b) 11 cm
c) 10 cm
d) 6 cm
Answer: a) 13 cm
Question: If △DEF ~ △XYZ and the sides of △DEF are 3 cm, 4 cm, and 5 cm, then the sides of △XYZ can be:
a) 6 cm, 8 cm, 10 cm
b) 9 cm, 12 cm, 15 cm
c) 12 cm, 16 cm, 20 cm
d) All of the above
Answer: d) All of the above
Question: The area of two similar triangles is in the ratio 4:9. The ratio of their corresponding sides is:
a) 2:3
b) 4:9
c) 8:27
d) 16:81
Answer: a) 2:3
Question: In △ABC, if AB = 6 cm, AC = 8 cm, and AD is the median, then BD/DC is:
a) 2/1
b) 1/2
c) 1/1
d) None of the above
Answer: c) 1/1
Question: In △PQR, if ∠P = 30°, ∠Q = 60°, then ∠R is:
a) 60°
b) 90°
c) 120°
d) 150°
Answer: b) 90°
Question: If in △ABC, ∠A = ∠C and AB = 6 cm, AC = 6 cm, then △ABC is:
a) Scalene
b) Isosceles
c) Equilateral
d) Right-angled
Answer: b) Isosceles
Question: The sum of the angles of a triangle is:
a) 90°
b) 120°
c) 180°
d) 360°
Answer: c) 180°
Question: If △ABC ~ △XYZ and the ratio of their areas is 1:9, then the ratio of their corresponding sides is:
a) 1:3
b) 1:9
c) 3:1
d) 9:1
Answer: a) 1:3
Question: The median of a triangle divides it into:
a) Two congruent triangles
b) Two similar triangles
c) Two triangles of equal area
d) None of the above
Answer: c) Two triangles of equal area
Question: In △ABC, if ∠B = 90°, BC = 4 cm, AC = 5 cm, then AB is:
a) 3 cm
b) 2 cm
c) 6 cm
d) 9 cm
Answer: a) 3 cm
Question: In △PQR, if PQ = QR, then the triangle is:
a) Scalene
b) Isosceles
c) Equilateral
d) None of the above
Answer: b) Isosceles
Question: In △ABC, if AB = 12 cm, AC = 16 cm, BC = 20 cm, then ∠A is:
a) 90°
b) 60°
c) 45°
d) 30°
Answer: a) 90°
Question: In △XYZ, if XY = 7 cm, XZ = 24 cm, and YZ = 25 cm, the triangle is:
a) Scalene
b) Isosceles
c) Right-angled
d) Equilateral
Answer: c) Right-angled
Question: The perimeter of an equilateral triangle with side length 6 cm is:
a) 6 cm
b) 12 cm
c) 18 cm
d) 24 cm
Answer: c) 18 cm
Question: If △ABC ~ △DEF, and the ratio of their corresponding sides is 1:2, then the ratio of their perimeters is:
a) 1:2
b) 1:4
c) 2:1
d) 1:1
Answer: a) 1:2
Question: In △PQR, if PR² = PQ² + QR², then △PQR is:
a) Right-angled
b) Equilateral
c) Isosceles
d) Scalene
Answer: a) Right-angled
Question: In △ABC, if ∠A = 60°, ∠B = 60°, then the triangle is:
a) Right-angled
b) Scalene
c) Isosceles
d) Equilateral
Answer: d) Equilateral
Question: In △DEF, if DE = 8 cm, EF = 15 cm, DF = 17 cm, then the triangle is:
a) Scalene
b) Isosceles
c) Equilateral
d) Right-angled
Answer: d) Right-angled
Question: In △ABC, if AB = AC = BC, then the triangle is:
a) Scalene
b) Isosceles
c) Equilateral
d) Right-angled
Answer: c) Equilateral
Question: If △PQR is right-angled at P, and PQ = 3 cm, PR = 4 cm, then QR is:
a) 5 cm
b) 6 cm
c) 7 cm
d) 8 cm
Answer: a) 5 cm
Question: In △ABC, if AB² + BC² < AC², then the triangle is:
a) Acute-angled
b) Right-angled
c) Obtuse-angled
d) Equilateral
Answer: c) Obtuse-angled
Question: The sum of the lengths of any two sides of a triangle is:
a) Less than the third side
b) Equal to the third side
c) Greater than the third side
d) None of the above
Answer: c) Greater than the third side
Question: In △ABC, if BC is the hypotenuse and AB² + AC² = BC², then △ABC is:
a) Right-angled
b) Equilateral
c) Isosceles
d) Scalene
Answer: a) Right-angled
Question: If △PQR is an equilateral triangle and PQ = 6 cm, then the area of △PQR is:
a) 18 cm²
b) 9√3 cm²
c) 36 cm²
d) 27√3 cm²
Answer: b) 9√3 cm²
Question: The altitude of an equilateral triangle of side 8 cm is:
a) 4 cm
b) 4√3 cm
c) 8 cm
d) 8√3 cm
Answer: b) 4√3 cm
Question: In △XYZ, if ∠X = 90° and XY = 6 cm, YZ = 10 cm, then XZ is:
a) 6 cm
b) 8 cm
c) 10 cm
d) 12 cm
Answer: b) 8 cm
Question: If in △ABC, ∠A = ∠B = ∠C, then the triangle is:
a) Isosceles
b) Scalene
c) Right-angled
d) Equilateral
Answer: d) Equilateral
