How many practice questions are available for Triangles?

SparkEd Math offers 60+ practice questions for Triangles 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.

Is Triangles content free on SparkEd Math?

Yes! All Triangles content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Triangles differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Triangles 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 Triangles content aligned with the CBSE syllabus?

Yes, all Triangles questions and lessons on SparkEd Math are fully aligned with the Central Board of Secondary Education (CBSE) syllabus for Class 9. The content follows the official curriculum structure and exam pattern.

Triangles — Class 9 CBSE (2025-26)

About Triangles — Class 9 CBSE

Study congruence rules, properties of isosceles triangles, and inequalities in triangles. This topic is part of the CBSE Class 9 mathematics syllabus (chapter: Chapter 7). 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

Introduction to Triangles and Congruence
Congruence Criteria: SSS and SAS
Congruence Criteria: ASA and RHS
Properties of Isosceles and Equilateral Triangles
Summary, NCERT Connections, and Practice Prep

Interactive lesson · about 15 minutes · checkpoint question after every unit

Triangles — solved examples for Class 9 CBSE

Example 1easy

Which of the following statements correctly defines congruent figures?

A)A) Figures that have the same shape but different sizes.
B)B) Figures that have the same size but different shapes.
C)C) Figures that have exactly the same shape and the same size.
D)D) Figures that are reflections of each other.

Step-by-step solution

Congruent figures are those that can be perfectly superimposed on each other without any distortion.
For this to happen, they must possess identical shapes and identical sizes.

Answer: C) Figures that have exactly the same shape and the same size.

Example 2medium

In ΔABC, if ∠A = 2x, ∠B = 3x - 10°, and ∠C = x + 40°, what is the measure of ∠A?

A)40°
B)50°
C)60°
D)70°

Step-by-step solution

According to the Angle Sum Property of a triangle, ∠A + ∠B + ∠C = 180°.
Substitute the given expressions: (2x) + (3x - 10°) + (x + 40°) = 180°.
Combine like terms and solve for x: 6x + 30° = 180° ⇒ 6x = 150° ⇒ x = 25°.
Now, calculate the measure of ∠A: ∠A = 2x = 2 × 25° = 50°.

Answer: 50°

Example 3hard

Two line segments AB and CD bisect each other at point O. Which congruence criterion can be used to prove that ΔAOC ≅ ΔBOD, and consequently, AC = BD?

A)SSS
B)SAS
C)ASA
D)RHS

Step-by-step solution

Given that AB and CD bisect each other at O, we have AO = OB and CO = OD.
Also, ∠AOC and ∠BOD are vertically opposite angles, so ∠AOC = ∠BOD.
Therefore, in ΔAOC and ΔBOD, we have two sides and the included angle equal (AO = OB, ∠AOC = ∠BOD, CO = OD).
By the SAS (Side-Angle-Side) congruence criterion, ΔAOC ≅ ΔBOD. Consequently, AC = BD by CPCTC.

Answer: SAS

Practice questions on Triangles

Q1.easy
If ΔPQR ≅ ΔXYZ, which of the following statements is NOT necessarily true?
1. A)A) PQ = XY
2. B)B) QR = YZ
3. C)C) ∠P = ∠X
4. D)D) PR = YZ
Show answer
Answer: D) PR = YZ
Hint: Remember that 'corresponding parts' means sides and angles that match up when the triangles are perfectly overlaid. The order of vertices in the congruence statement matters.
Q2.easy
To prove ΔABC ≅ ΔDEF using the SSS (Side-Side-Side) congruence criterion, if we are given AB = DE and BC = EF, what additional information is required?
1. A)A) ∠B = ∠E
2. B)B) AC = DF
3. C)C) ∠C = ∠F
4. D)D) AB = EF
Show answer
Answer: B) AC = DF
Hint: The SSS criterion requires all three pairs of corresponding sides to be equal.
Q3.easy
Rohan is trying to prove that ΔPQR ≅ ΔSTU using the SAS (Side-Angle-Side) congruence criterion. He states that PQ = ST, PR = SU, and ∠Q = ∠T. What is the mistake in Rohan's reasoning?
1. A)A) He should have used SSS criterion instead.
2. B)B) The angle must be the included angle between the two sides. ∠Q is not included between PQ and PR.
3. C)C) The sides chosen (PQ and PR) are incorrect for SAS.
4. D)D) The triangles cannot be proven congruent with the given information.
Show answer
Answer: B) The angle must be the included angle between the two sides. ∠Q is not included between PQ and PR.
Hint: Remember that in SAS, the angle must be *included* between the two sides that are given as equal.
Q4.medium
In ΔPQR, if PQ = PR and ∠Q = 50°, what is the measure of ∠P?
1. A)50°
2. B)60°
3. C)70°
4. D)80°
Show answer
Answer: 80°
Hint: Recall the property of angles opposite to equal sides in an isosceles triangle.
Q5.medium
Two triangles, ΔABC and ΔXYZ, are congruent by the SAS criterion. If AB = XY and ∠B = ∠Y, then which of the following must also be true for congruence?
1. A)AC = XZ
2. B)BC = YZ
3. C)∠A = ∠X
4. D)∠C = ∠Z
Show answer
Answer: BC = YZ
Hint: For SAS congruence, the angle must be *included* between the two sides.
Q6.medium
In quadrilateral ABCD, AC is a diagonal. If AB = CD and BC = DA, which congruence criterion proves ΔABC ≅ ΔCDA?
1. A)SAS
2. B)ASA
3. C)SSS
4. D)RHS
Show answer
Answer: SSS
Hint: Look for all three pairs of corresponding sides to be equal.
Q7.hard
In ΔABC, AB = AC. The bisectors of ∠B and ∠C intersect at O. If ∠BAC = 40°, what is the measure of ∠BOC?
1. A)110°
2. B)120°
3. C)130°
4. D)140°
Show answer
Answer: 110°
Hint: First, find the base angles of the isosceles triangle. Then use the angle bisector property and the angle sum property in the smaller triangle.
Q8.hard
Ravi was trying to prove that if two altitudes of a triangle are equal, then the triangle is isosceles. He considered ΔABC with altitudes AD ⊥ BC and BE ⊥ AC. Given AD = BE, Ravi wrote the following steps to prove AC = BC:
1. Consider ΔADC and ΔBEC.
2. ∠ADC = ∠BEC = 90°.
3. AD = BE (Given).
4. AC = BC (Hypotenuse).
5. Therefore, ΔADC ≅ ΔBEC by RHS congruence criterion.
Where is Ravi's mistake?
1. A)Step 1: He chose the wrong triangles.
2. B)Step 2: ∠ADC and ∠BEC are not always 90°.
3. C)Step 3: AD = BE is a conclusion, not a given.
4. D)Step 4: He assumed AC = BC, which is what he needed to prove.
Show answer
Answer: Step 4: He assumed AC = BC, which is what he needed to prove.
Hint: In a proof, you cannot use the conclusion as one of your premises. The hypotenuse in RHS must be a given equal side or a common side.
Q9.hard
In ΔABC, AD is the altitude from A to BC, and BE is the altitude from B to AC. If AD = BE, which congruence criterion is most suitable to prove that ΔABD ≅ ΔBAE?
1. A)SSS
2. B)SAS
3. C)ASA
4. D)RHS
Show answer
Answer: RHS
Hint: Altitudes imply right angles. Look for a common side that serves as the hypotenuse in both right-angled triangles.

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.