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SparkEd Math offers 60+ practice questions for Triangle and Its Properties across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

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SparkEd Math uses visual step-by-step solutions for every Triangle and Its Properties problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Triangle and Its Properties content aligned with the Olympiad syllabus?

Yes, all Triangle and Its Properties questions and lessons on SparkEd Math are fully aligned with the Mathematical Olympiad Preparation (Olympiad) syllabus for Class 7. The content follows the official curriculum structure and exam pattern.

Triangle and Its Properties — Class 7 Olympiad (2025-26)

About Triangle and Its Properties — Class 7 Olympiad

Apply angle sum property, triangle inequality, Pythagoras theorem, and solve competition-level triangle problems. This topic is part of the Olympiad Class 7 mathematics syllabus (chapter: Module 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.

Triangle and Its Properties — solved examples for Class 7 Olympiad

Example 1easy

In a triangle PQR, the measures of the angles are in the ratio 2:3:5. What is the measure of the smallest angle in degrees?

A)36°
B)54°
C)90°
D)18°

Step-by-step solution

Let the angles of the triangle PQR be 2x, 3x, and 5x.
According to the angle sum property of a triangle, the sum of all interior angles is 180°.
$2x + 3x + 5x = 180°$
Combine the terms: 10x = 180°.
Solve for x: x = 180° / 10 = 18°.
The smallest angle is 2x = 2 × 18° = 36°.

Answer: 36°

Example 2medium

In an isosceles triangle, one of the base angles is 15° less than the vertex angle. What is the measure of the largest angle in this triangle?

A)A) 50°
B)B) 60°
C)C) 65°
D)D) 70°

Step-by-step solution

Let the vertex angle be V and the base angles be B. In an isosceles triangle, the base angles are equal.
According to the problem, one base angle is 15° less than the vertex angle: B = V - 15°.
Using the angle sum property: V + B + B = 180°, which simplifies to V + 2B = 180°.
Substitute B = V - 15° into the sum equation: V + 2(V - 15°) = 180°.
$V + 2(V - 15°) = 180°$
Solve for V: V + 2V - 30° = 180° => 3V = 210° => V = 70°.
Calculate the base angles: B = 70° - 15° = 55°.
The angles of the triangle are 70°, 55°, 55°. The sum is 70° + 55° + 55° = 180°.
The largest angle in this triangle is the vertex angle, which is 70°.

Answer: D) 70°

Example 3hard

In triangle ABC, AB = AC. The angle bisectors of ∠B and ∠C meet at point O. If ∠BOC = 110°, find the measure of ∠BAC.

A)40°
B)50°
C)60°
D)70°

Step-by-step solution

In ΔBOC, the sum of angles is 180°. So, ∠OBC + ∠OCB + 110° = 180°, which means ∠OBC + ∠OCB = 70°.
Since BO and CO are angle bisectors, ∠ABC = 2∠OBC and ∠ACB = 2∠OCB. Therefore, ∠ABC + ∠ACB = 2(∠OBC + ∠OCB) = 2 × 70° = 140°.
In ΔABC, AB = AC, so it's an isosceles triangle, meaning ∠ABC = ∠ACB. Thus, each of these angles is 140°/2 = 70°.
Using the angle sum property for ΔABC: ∠BAC + ∠ABC + ∠ACB = 180°. So, ∠BAC + 70° + 70° = 180°, which gives ∠BAC + 140° = 180°. Therefore, ∠BAC = 40°.

Answer: 40°

Practice questions on Triangle and Its Properties

Q1.easy
In triangle ABC, side BC is extended to point D. If the exterior angle ∠ACD = 115° and ∠B = 60°, what is the measure of the interior angle ∠A?
1. A)55°
2. B)60°
3. C)65°
4. D)70°
Show answer
Answer: 55°
Hint: The exterior angle of a triangle is equal to the sum of its two opposite interior angles.
Q2.easy
Which of the following sets of side lengths CANNOT form a triangle?
1. A)7 cm, 10 cm, 5 cm
2. B)3 cm, 4 cm, 5 cm
3. C)6 cm, 2 cm, 3 cm
4. D)8 cm, 8 cm, 8 cm
Show answer
Answer: 6 cm, 2 cm, 3 cm
Hint: For any three lengths to form a triangle, the sum of the lengths of any two sides must be strictly greater than the length of the third side.
Q3.easy
A ladder 13 meters long is placed against a wall. If the foot of the ladder is 5 meters away from the base of the wall, how high up the wall does the ladder reach?
1. A)8 meters
2. B)10 meters
3. C)12 meters
4. D)14 meters
Show answer
Answer: 12 meters
Hint: Visualize the situation as a right-angled triangle where the ladder is the hypotenuse.
Q4.medium
In triangle PQR, the exterior angle at Q is 125°. If ∠P is 15° more than ∠R, what is the measure of ∠Q?
1. A)A) 55°
2. B)B) 60°
3. C)C) 65°
4. D)D) 70°
Show answer
Answer: A) 55°
Hint: Remember that the exterior angle of a triangle is equal to the sum of its two opposite interior angles.
Q5.medium
The lengths of two sides of a triangle are 5 cm and 12 cm. If the third side is an integer, what is the minimum possible perimeter of the triangle?
1. A)A) 22 cm
2. B)B) 23 cm
3. C)C) 24 cm
4. D)D) 25 cm
Show answer
Answer: D) 25 cm
Hint: Use the Triangle Inequality Theorem to determine the smallest possible integer length for the third side.
Q6.medium
A square field has a diagonal path of 20√2 meters. If a person walks along two sides of the square instead of the diagonal path, how much extra distance do they cover?
1. A)A) 10(2 - √2) m
2. B)B) 20(2 - √2) m
3. C)C) 20√2 m
4. D)D) 40 m
Show answer
Answer: B) 20(2 - √2) m
Hint: For a square, the diagonal forms a right-angled isosceles triangle with two sides. Use the Pythagorean theorem or the property of square diagonals.
Q7.hard
In triangle ABC, AB = AC. Point D is on AC such that BD = BC. Point E is on AB such that AE = AD. If ∠BAC = 40°, find the measure of ∠BDE.
1. A)30°
2. B)40°
3. C)45°
4. D)50°
Show answer
Answer: 40°
Hint: Use the isosceles triangle properties and the exterior angle property repeatedly. Start with ΔABC to find ∠ABC and ∠ACB.
Q8.hard
Two sides of a triangle have lengths 8 cm and 15 cm. If the third side is an integer, what is the maximum possible integer value for the perimeter of the triangle?
1. A)43 cm
2. B)45 cm
3. C)46 cm
4. D)47 cm
Show answer
Answer: 45 cm
Hint: Use the triangle inequality theorem to find the range of possible values for the third side. Remember to consider the maximum integer value within that range.
Q9.hard
An isosceles triangle has two equal sides of length 13 cm and a base of 24 cm. What is the length of the altitude drawn from the vertex connecting the equal sides to the base?
1. A)5 cm
2. B)6 cm
3. C)7 cm
4. D)8 cm
Show answer
Answer: 5 cm
Hint: The altitude from the vertex to the base of an isosceles triangle bisects the base. This creates two right-angled triangles.

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