Triangles (Class 10 Mathematics)
Triangles are fundamental geometric shapes, and understanding their properties like similarity, congruence, and the Pythagorean theorem is essential for ge
TL;DR: Triangles are fundamental geometric shapes, and understanding their properties like similarity, congruence, and the Pythagorean theorem is essential f…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
Triangles are fundamental geometric shapes, and understanding their properties like similarity, congruence, and the Pythagorean theorem is essential for ge
Triangles MCQs with Answers & Explanations
Q1. If two triangles are similar, then their corresponding angles are:
- Supplementary
- Proportional
- Complementary
- Equal ✓ (correct)
Explanation: If two triangles are similar, their corresponding angles are equal and corresponding sides are proportional.
Q2. The basic proportionality theorem states that if a line is drawn parallel to one side of a triangle, then it divides the other two sides:
- Proportionally ✓ (correct)
- Equally
- In ratio 1:1
- At their midpoints
Explanation: The basic proportionality theorem (Thales' theorem) states that a line parallel to one side divides the other two sides proportionally.
Q3. If in triangle ABC, AB = 3 cm, BC = 4 cm, and AC = 5 cm, then triangle ABC is:
- Equilateral
- Right-angled ✓ (correct)
- Obtuse-angled
- Acute-angled
Explanation: Since 3^2 + 4^2 = 9 + 16 = 25 = 5^2, triangle ABC is right-angled at B.
Q4. The area of a triangle with sides a, b, and c is given by:
- a x b x c
- sqrt(a^2 + b^2 - 2ab cosC)
- sqrt(s(s-a)(s-b)(s-c)) ✓ (correct)
- (1/2) x base x height
Explanation: Heron's formula gives the area of a triangle as sqrt(s(s-a)(s-b)(s-c)) where s = (a+b+c)/2.
Q5. If triangle ABC is similar to triangle PQR, and AB:PQ = 2:3, then the ratio of their areas is:
- 2:3
- 8:27
- 6:9
- 4:9 ✓ (correct)
Explanation: The ratio of areas of similar triangles is the square of the ratio of corresponding sides: (2/3)^2 = 4/9.
Q6. Two triangles are congruent if:
- SSS, SAS, ASA, or AAS conditions are satisfied ✓ (correct)
- They are similar
- Their corresponding angles are equal
- They have the same area
Explanation: Two triangles are congruent if they satisfy any of the congruence criteria: SSS, SAS, ASA, AAS, or RHS.
Q7. In a right-angled triangle, if the hypotenuse is 13 cm and one side is 5 cm, the other side is:
- 8 cm
- 12 cm ✓ (correct)
- 10 cm
- 9 cm
Explanation: Using Pythagorean theorem: other side = sqrt(13^2 - 5^2) = sqrt(169 - 25) = sqrt(144) = 12 cm.
Q8. The angle bisector theorem states that the angle bisector divides the opposite side in the ratio of:
- 1:1
- The altitudes
- The adjacent sides ✓ (correct)
- The other two angles
Explanation: The angle bisector theorem states that the angle bisector divides the opposite side in the ratio of the adjacent sides.
Q9. If the altitude from vertex A to side BC of triangle ABC is 6 cm and BC = 8 cm, the area is:
- 48 cm^2
- 12 cm^2
- 36 cm^2
- 24 cm^2 ✓ (correct)
Explanation: Area of triangle = (1/2) x base x height = (1/2) x 8 x 6 = 24 cm^2.
Q10. If triangle ABC has sides 6 cm, 8 cm, and 10 cm, then the radius of its circumcircle is:
- 5 cm ✓ (correct)
- 3 cm
- 6 cm
- 4 cm
Explanation: For a right-angled triangle, the circumradius = hypotenuse/2 = 10/2 = 5 cm.
Frequently Asked Questions
What is the difference between similar and congruent triangles?
Congruent triangles have the same size and shape, while similar triangles have the same shape but different sizes.
How is the Pythagorean theorem used to determine if a triangle is right-angled?
If the square of the longest side equals the sum of squares of the other two sides, the triangle is right-angled.
More Class 10 Mathematics MCQs
🤖 Stuck on any of these? Ask Syllab's free AI Tutor to explain step by step →