Triangles
22 solved questions from Class 10 Mathematics, each with the full working. Tap any question to see the step-by-step solution.
- 1 In a △ ABC, DE ∥ BC such that D lies on AB and E lies on AC. If AD = 3.6 cm, DB = 2.4 cm, and EC = 3 cm, find the length of AE. easy MCQ 1 mark Basic Proportionality Theorem (Thales Theorem)
- 2 BL and CM are medians of a triangle ABC right-angled at A. Prove that 4(BL^2 + CM^2) = 5BC^2. hard 5 marks Pythagoras Theorem applied to medians of a right triangle
- 3 In a quadrilateral ABCD, diagonals AC and BD intersect each other at point O such that AO/BO = CO/DO. Prove that ABCD is a trapezium. medium 3 marks Converse of Basic Proportionality Theorem
- 4 Triangle MNO has vertices M(2,3), N(8,-1) and O(5,7). Find the length of the altitude from vertex O to side MN. Give your answer correct to two decimal places (in units). hard 3 marks Altitude length using area and coordinate geometry
- 5 The sides of triangle XYZ are 13 cm, 14 cm and 15 cm. Find its area (in cm^2). medium 2 marks Heron's formula for area
- 6 In triangle PQR, a line through point S on side PQ is drawn parallel to QR intersecting PR at T. If PS = 4 cm, SQ = 6 cm and QR = 15 cm, find the length of ST (in cm). easy 1 mark Similarity of triangles with parallel line
- 7 What is the sum of all interior angles of a triangle? medium MCQ Angle Sum Property
- 8 What is the sum of interior angles of a quadrilateral? medium MCQ Polygon Angles
- 9 In a right triangle with legs 3 cm and 4 cm, find hypotenuse length. medium MCQ Pythagoras Theorem
- 10 How many tangents can be drawn to a circle from an external point? medium MCQ Tangents to Circle
- 11 What is the angle between a tangent and the radius at the point of contact? medium MCQ Tangent Properties
- 12 Two triangles are similar if their corresponding sides are in ____. medium MCQ Similar Triangles
- 13 Find the perimeter of a square with side length 6 cm. medium MCQ Perimeter of Square
- 14 What is the formula for area of a circle with radius r? medium MCQ Area of Circle
- 15 If diameter of a circle is 14 cm, what is its radius? medium MCQ Circle Definitions
- 16 State Pythagoras Theorem for a right-angled triangle. medium MCQ Pythagoras Theorem
- 17 What is the domain, range, or fundamental theorem introduced in 'Triangles' (Class 10 Mathematics)? medium MCQ Functions & Theorems
- 18 What is the derivative or integral formula associated with 'Triangles'? medium MCQ Calculus & Formulae
- 19 How do you find the solution set or optimum value in 'Triangles'? medium MCQ Problem Solving & Optimization
- 20 Find the area of a right‑angled triangle whose legs are 5 cm and 12 cm. easy 1 mark Area of right triangle
- 21 In the right‑angled triangle ABC, the sides are 9 cm, 12 cm and 15 cm. Find the length of the median drawn from the right angle to the hypotenuse. medium 2 marks Median to hypotenuse in right triangle
- 22 Triangle PQR has sides 6 cm, 8 cm and 10 cm. Triangle XYZ is similar to triangle PQR with a scale factor of 2. Which of the following gives the area of triangle XYZ? medium MCQ 3 marks Area scaling in similar triangles