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About Triangles — Class 9 ICSE

Study triangle properties including inequality, angle sum, exterior angle, and congruence criteria. This topic is part of the ICSE Class 9 mathematics syllabus (chapter: Chapter 8). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Triangles

  • Congruence of Triangles
  • Congruence Criteria: SSS, SAS, ASA, RHS
  • Properties of Isosceles and Equilateral Triangles
  • Mid-Point Theorem and Similar Triangles
  • Pythagoras Theorem and Applications

Interactive lesson · about 20 minutes · checkpoint question after every unit

Triangles — solved examples for Class 9 ICSE

Example 1easy

What is the sum of all interior angles of a triangle?
  1. A)90°
  2. B)180°
  3. C)270°
  4. D)360°

Step-by-step solution

  1. The angle sum property states that the sum of all interior angles of any triangle is always 180°.
  2. This can be proven by drawing a line parallel to the base through the opposite vertex.
    ∠A+∠B+∠C=180°∠A + ∠B + ∠C = 180°

Answer: 180°

Example 2medium

In triangle ABC, ∠A = 2x + 10°, ∠B = 3x, and ∠C = x + 20°. Find x.
  1. A)20°
  2. B)25°
  3. C)30°
  4. D)35°

Step-by-step solution

  1. Using angle sum property:
    ∠A+∠B+∠C=180°∠A + ∠B + ∠C = 180°
  2. Substitute:
    (2x+10)+3x+(x+20)=180(2x + 10) + 3x + (x + 20) = 180
  3. Combine like terms:
    6x+30=1806x + 30 = 180
  4. Solve:
    6x=150→x=25°6x = 150 → x = 25°

Answer: 25°

Example 3hard

In triangle PQR, ∠P = (3x - 5)°, ∠Q = (2x + 15)°, and ∠R = (x + 20)°. Find the type of triangle by its angles.
  1. A)Acute
  2. B)Right
  3. C)Obtuse
  4. D)Equilateral

Step-by-step solution

  1. Sum of angles:
    (3x−5)+(2x+15)+(x+20)=180(3x-5) + (2x+15) + (x+20) = 180
  2. Simplify:
    6x+30=180→x=256x + 30 = 180 → x = 25
  3. ∠P = 3(25)-5 = 70°, ∠Q = 2(25)+15 = 65°, ∠R = 25+20 = 45°
  4. All angles < 90°, so it's an acute triangle.

Answer: Acute

Practice questions on Triangles

  1. Q1.easy

    In a triangle, two angles measure 65° and 45°. What is the third angle?
    1. A)60°
    2. B)70°
    3. C)80°
    4. D)75°
    Show answer

    Answer: 70°

    Hint: Use the angle sum property: subtract the known angles from 180°.

  2. Q2.easy

    A triangle with all three sides equal is called:
    1. A)Isosceles triangle
    2. B)Scalene triangle
    3. C)Equilateral triangle
    4. D)Right triangle
    Show answer

    Answer: Equilateral triangle

    Hint: 'Equi' means equal and 'lateral' means side.

  3. Q3.easy

    What is each angle of an equilateral triangle?
    1. A)45°
    2. B)60°
    3. C)90°
    4. D)120°
    Show answer

    Answer: 60°

    Hint: All three angles are equal, and they must sum to 180°.

  4. Q4.medium

    An exterior angle of a triangle is 120°. If one of the non-adjacent interior angles is 50°, find the other non-adjacent interior angle.
    1. A)60°
    2. B)70°
    3. C)80°
    4. D)50°
    Show answer

    Answer: 70°

    Hint: Use the exterior angle theorem: exterior angle = sum of the two non-adjacent interior angles.

  5. Q5.medium

    The sides of a triangle are 5 cm, 12 cm, and 13 cm. Is it a right triangle?
    1. A)Yes
    2. B)No
    3. C)Cannot determine
    4. D)Only if angles are given
    Show answer

    Answer: Yes

    Hint: Check if the Pythagorean theorem holds: does a² + b² = c²?

  6. Q6.medium

    In an isosceles triangle, the vertex angle is 40°. Find each base angle.
    1. A)60°
    2. B)70°
    3. C)80°
    4. D)50°
    Show answer

    Answer: 70°

    Hint: The two base angles are equal. Use the angle sum property.

  7. Q7.hard

    The sides of a triangle are (2x + 1), (3x - 2), and (x + 5) cm. If the perimeter is 34 cm, find the sides.
    1. A)11, 13, 10
    2. B)9, 13, 12
    3. C)11, 11, 12
    4. D)7, 10, 17
    Show answer

    Answer: 11, 13, 10

    Hint: Perimeter = sum of all sides. Set up the equation and solve for x.

  8. Q8.hard

    In a right triangle, the hypotenuse is 25 cm and one leg is 7 cm. Find the other leg.
    1. A)18 cm
    2. B)24 cm
    3. C)20 cm
    4. D)22 cm
    Show answer

    Answer: 24 cm

    Hint: Use Pythagoras: other leg² = hypotenuse² - known leg².

  9. Q9.hard

    Two angles of a triangle are complementary. What is the third angle?
    1. A)45°
    2. B)60°
    3. C)90°
    4. D)180°
    Show answer

    Answer: 90°

    Hint: Complementary angles sum to 90°. What's left for the third angle?

These are 9 of the 60 questions available for Triangles. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.