Triangles — Class 10 MCQs with Answers

Triangles — important questions & MCQs with answers (Class 10 Mathematics)

14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 76 are timed and scored when you sign in.

1. Q1Easy

   Two triangles are similar if their corresponding angles are equal and corresponding sides are:

   A.Equal

   B.Perpendicular

   C.Proportional✓ Correct

   D.Parallel

   Answer: C. Proportional

   Explanation: Similar triangles need equal corresponding angles AND proportional corresponding sides — equal sides alone would make them congruent, not just similar.

2. Q2Easy

   BPT (Basic Proportionality Theorem) is also known as:

   A.Thales Theorem✓ Correct

   B.Pythagoras Theorem

   C.Mid-point Theorem

   D.Angle Sum Theorem

   Answer: A. Thales Theorem

   Explanation: The Basic Proportionality Theorem is called Thales' Theorem after the Greek mathematician who first proved that a line parallel to one side of a triangle divides the other two proportionally.

3. Q3Easy

   Basic Proportionality Theorem states: If a line is drawn parallel to one side of a triangle to intersect the other two sides, then:

   A.The other two sides are divided in the same ratio✓ Correct

   B.The triangle is right-angled

   C.The line equals half the third side

   D.All sides become equal

   Answer: A. The other two sides are divided in the same ratio

   Explanation: Basic Proportionality (Thales') Theorem: a line parallel to one side of a triangle divides the other two sides in the same ratio.

4. Q4Easy

   In a right triangle, the square of the hypotenuse equals:

   A.Difference of squares

   B.Sum of squares of the other two sides✓ Correct

   C.Product of the other two sides

   D.Twice the area

   Answer: B. Sum of squares of the other two sides

   Explanation: Pythagoras theorem: in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.

5. Q5Easy

   Two triangles are similar if:

   A.Their areas are equal

   B.Their corresponding sides are equal

   C.Their corresponding angles are equal and corresponding sides are proportional✓ Correct

   D.They are congruent only

   Answer: C. Their corresponding angles are equal and corresponding sides are proportional

   Explanation: AA similarity: if corresponding angles are equal, corresponding sides are automatically proportional, and vice versa — equal sides alone (congruence) is a stricter, different condition.

6. Q6Easy

   If in two triangles the corresponding angles are equal, the triangles are similar by the criterion known as:

   A.SSS congruence

   B.AAA similarity✓ Correct

   C.RHS congruence

   D.ASA congruence

   Answer: B. AAA similarity

   Explanation: When corresponding angles of two triangles are equal their corresponding sides are in the same ratio, which is the AAA similarity criterion.

7. Q7Medium

   Areas of two similar triangles are 64 cm² and 121 cm². Ratio of corresponding sides:

   A.2:3

   B.64:121

   C.4:9

   D.8:11✓ Correct

   Answer: D. 8:11

   Explanation: Area ratio equals (side ratio)², so side ratio = √(64/121) = 8/11 — squaring, not halving, the area ratio; picking 64:121 directly ignores the square-root step.

8. Q8Medium

   In a right triangle, hypotenuse=13, one side=5. The other side =

   A.8

   B.10

   C.12✓ Correct

   D.9

   Answer: C. 12

   Explanation: By Pythagoras theorem, the missing leg = √(hypotenuse² − leg²) = √(13² − 5²) = √144 = 12.

9. Q9Medium

   In ΔABC, DE ∥ BC, AD = 4, DB = 6, AE = 6. Then EC equals:

   A.4

   B.6

   C.9✓ Correct

   D.12

   Answer: C. 9

   Explanation: By the Basic Proportionality Theorem, DE ∥ BC gives AD/DB = AE/EC, so 4/6 = 6/EC, and cross-multiplying gives EC = 36/4 = 9.

10. Q10Medium

    A ladder 13 m long reaches a window 12 m above the ground. Distance of its foot from the wall is:

    A.5 m✓ Correct

    B.6 m

    C.7 m

    D.8 m

    Answer: A. 5 m

    Explanation: By Pythagoras theorem, the foot's distance = √(13² − 12²) = √(169 − 144) = √25 = 5 m.

11. Q11Medium

    In two similar triangles, ratio of areas is 16 : 25. Ratio of their corresponding sides is:

    A.4 : 5✓ Correct

    B.16 : 25

    C.2 : 5

    D.4 : 25

    Answer: A. 4 : 5

    Explanation: Since area ratio = (side ratio)², side ratio = √(16/25) = 4/5 — take the square root of the area ratio, don't use it directly.

12. Q12Hard

    If △ABC ~ △DEF with AB=4, DE=6, area(ABC)=16. area(DEF)=?

    A.36✓ Correct

    B.24

    C.48

    D.32

    Answer: A. 36

    Explanation: Since ΔABC ~ ΔDEF, area ratio = (AB/DE)² = (4/6)² = 4/9, so area(DEF) = 16 × 9/4 = 36 — using the side ratio 4/6 directly instead of squaring it gives the wrong option.

13. Q13Hard

    Sides 5, 12, 13. The triangle is:

    A.Acute

    B.Obtuse

    C.Right-angled✓ Correct

    D.Equilateral

    Answer: C. Right-angled

    Explanation: By the converse of Pythagoras theorem, since 5² + 12² = 25 + 144 = 169 = 13², the triangle must be right-angled, with the right angle opposite the longest side.

14. Q14Hard

    In ΔABC, points D and E are on AB and AC respectively such that DE ∥ BC. If AD = 2 cm, DB = 3 cm and AC = 10 cm, then EC equals:

    A.6 cm✓ Correct

    B.4 cm

    C.8 cm

    D.5 cm

    Answer: A. 6 cm

    Explanation: By BPT, AE/EC = AD/DB = 2/3. With AE + EC = AC = 10, splitting in ratio 2:3 gives AE = 4 and EC = 6 cm.

Triangles — FAQs

More Class 10 Mathematics chapters

• 01Real Numbers
• 02Polynomials
• 03Pair of Linear Equations in Two Variables
• 04Quadratic Equations
• 05Arithmetic Progressions
• 07Coordinate Geometry

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