Triangles — Class 9 MCQs with Answers
Class 9 CBSE Mathematics · Chapter 12
90 practice questions · 30 Easy · 30 Medium · 30 Hard · Updated
Practise the most important Class 9 CBSE Mathematics questions from Chapter 12, "Triangles". You get 9 timed quizzes made from 90 NCERT-based MCQs, with answers and explanations. The questions are split into 30 Easy, 30 Medium and 30 Hard. Warm up on the basics, then move on to the exam-level questions that set top scorers in CBSE Board exams and the JEE & NEET foundation years apart.
To score well in "Triangles", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This trains you to stay accurate under time pressure, as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.
Use this chapter for focused revision. Start with the Easy set to check your basics on Triangles, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 9 Mathematics mastery score. 14 sample questions are solved in full below, with the answer and a worked explanation. Sign in free to start practising.
Key concepts: Triangles (Class 9 Mathematics)
Two triangles are congruent when one can be laid exactly on the other, and four criteria settle it without checking all six parts. This chapter proves the congruence criteria, uses them to establish properties of isosceles triangles, and derives the inequalities relating sides and angles.
- Congruent figures
- Figures identical in both shape and size, so that one covers the other exactly when superposed.
- Corresponding parts
- Matched vertices, sides and angles of two congruent triangles; the order of letters in the congruence statement records the matching.
- SAS criterion
- Two triangles are congruent when two sides and the INCLUDED angle of one equal the corresponding parts of the other.
- ASA criterion
- Two triangles are congruent when two angles and the included side of one equal the corresponding parts of the other.
Triangles — important questions & MCQs with answers (Class 9 Mathematics)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 76 are timed and scored when you sign in.
- Q1Easy
Two triangles are congruent by SAS if:
A.Two sides and the included angle are equal✓ CorrectB.Three sides are equalC.Two angles and any side are equalD.Two sides and a non-included angle are equalAnswer: A. Two sides and the included angle are equal
Explanation: SAS congruence needs the equal angle to lie between the two equal sides (the included angle) — two sides plus a non-included angle, SSA, is not a valid test.
- Q2Easy
In an isosceles triangle, the angles opposite to equal sides are:
A.Equal✓ CorrectB.SupplementaryC.ComplementaryD.Always 60°Answer: A. Equal
Explanation: This is the isosceles triangle theorem: the angles opposite the two equal sides are always equal to each other, whatever the size of the third angle.
- Q3Easy
Sum of any two sides of a triangle is:
A.Less than the third sideB.Equal to the third sideC.Half the third sideD.Greater than the third side✓ CorrectAnswer: D. Greater than the third side
Explanation: This is the triangle inequality: the sum of any two sides must exceed the third, otherwise the two shorter sides could not stretch far enough to close the triangle.
- Q4Easy
ASA congruence criterion requires:
A.Two sides and included angleB.Three sides equalC.Two angles and the included side equal✓ CorrectD.Any two angles equalAnswer: C. Two angles and the included side equal
Explanation: ASA needs the equal side to lie between the two equal angles (the included side); if the side sits outside them, the correct test is AAS, not ASA.
- Q5Easy
CPCT stands for:
A.Central Parts of Congruent TrianglesB.Corresponding Parts of Congruent Triangles✓ CorrectC.Congruent Parts of Corresponding TrianglesD.Common Parts of Congruent TrianglesAnswer: B. Corresponding Parts of Congruent Triangles
Explanation: CPCT means Corresponding Parts of Congruent Triangles — once two triangles are proven congruent by SSS/SAS/ASA/AAS/RHS, every matching side and angle pair is automatically equal.
- Q6Easy
In a triangle, the side opposite to the larger angle is:
A.SmallerB.EqualC.Larger✓ CorrectD.The medianAnswer: C. Larger
Explanation: The bigger the angle, the more the triangle opens up opposite it, so the side facing the larger angle is always the longer one.
- Q7Medium
In ΔABC and ΔPQR, AB=PQ=3cm, BC=QR=4cm, and ∠B=∠Q=60°. Are they congruent? By which criterion?
A.Yes, by SAS✓ CorrectB.Yes, by SSSC.Yes, by ASAD.Not congruentAnswer: A. Yes, by SAS
Explanation: AB=PQ and BC=QR are the two sides, and ∠B=∠Q — the angle between AB and BC — is the included angle, so this is exactly SAS congruence.
- Q8Medium
In isosceles ΔABC, AB=AC, and ∠A = 40°. Find ∠B.
A.40°B.70°✓ CorrectC.80°D.140°Answer: B. 70°
Explanation: Since AB=AC, base angles ∠B and ∠C are equal. With ∠A=40°, the angle sum gives 40°+2∠B=180°, so ∠B=70°.
- Q9Medium
Which set of sides can form a triangle?
A.3 cm, 4 cm, 8 cmB.1 cm, 2 cm, 3 cmC.5 cm, 7 cm, 9 cm✓ CorrectD.2 cm, 3 cm, 6 cmAnswer: C. 5 cm, 7 cm, 9 cm
Explanation: Checking the triangle inequality for each set: only 5, 7 and 9 cm hold in every combination (5+7>9, 5+9>7, 7+9>5); 3+4=7 is not greater than 8, so that set fails.
- Q10Medium
In right-angled triangles ABC and PQR, ∠B=∠Q=90°, AC=PR (hypotenuse), and BC=QR. By which criterion are they congruent?
A.SASB.ASAC.RHS✓ CorrectD.SSSAnswer: C. RHS
Explanation: With ∠B=∠Q=90°, hypotenuse AC=PR, and leg BC=QR equal, all three RHS conditions — Right angle, Hypotenuse, Side — are met.
- Q11Medium
ΔABC ≅ ΔPQR by SAS. If AB=4cm, BC=5cm, AC=6cm, find PQ.
A.4 cm✓ CorrectB.5 cmC.6 cmD.Cannot determineAnswer: A. 4 cm
Explanation: By CPCT, corresponding sides of congruent triangles are equal; since the correspondence is A↔P, B↔Q, C↔R, side PQ matches AB, so PQ=4 cm.
- Q12Hard
In ΔABC, AB=AC. D is the midpoint of BC. Prove AD bisects ∠A. Which of the following correctly uses this?
A.∠BAD=∠CAD because D is midpointB.∠BAD=∠CAD by CPCT since ΔABD≅ΔACD by SSS✓ CorrectC.AD=BD by CPCTD.ΔABD≅ΔACD by SAS onlyAnswer: B. ∠BAD=∠CAD by CPCT since ΔABD≅ΔACD by SSS
Explanation: AB=AC (given), BD=DC (D is the midpoint) and AD=AD (common) give SSS congruence between ΔABD and ΔACD, so CPCT makes ∠BAD=∠CAD.
- Q13Hard
Prove: The perimeter of a triangle is greater than the sum of its medians. If medians are 5,6,7 cm, the perimeter must be greater than:
A.9 cmB.12 cmC.18 cm✓ CorrectD.24 cmAnswer: C. 18 cm
Explanation: The three medians sum to 5+6+7=18 cm, and since a triangle's perimeter always exceeds the sum of its medians, the perimeter here must exceed 18 cm.
- Q14Hard
In ΔABC, the exterior angle at vertex A is 120° and ∠B = 80°. Find ∠C.
A.40°✓ CorrectB.60°C.80°D.20°Answer: A. 40°
Explanation: An exterior angle and its interior angle are supplementary, so ∠A = 180° − 120° = 60°. The angle sum then gives ∠C = 180° − 60° − 80° = 40°.
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Start this chapter free →Triangles — FAQs
What are the key concepts in Class 9 Mathematics Triangles?+
Two triangles are congruent when one can be laid exactly on the other, and four criteria settle it without checking all six parts. This chapter proves the congruence criteria, uses them to establish properties of isosceles triangles, and derives the inequalities relating sides and angles. Key ideas include Congruent figures, Corresponding parts, SAS criterion, ASA criterion.
What does Class 9 Mathematics Chapter 12 (Triangles) cover on XamBaaz?+
It has 90 NCERT-based MCQs on "Triangles": 30 Easy, 30 Medium and 30 Hard. Together they make 9 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE Board exams and the JEE & NEET foundation years.
Are these "Triangles" questions free to practise?+
Yes. Sign in with Google to practise "Triangles" free. Full unlimited access is ₹999/year on a launch offer until 1 December 2026. No chapter is charged separately.
How should I revise "Triangles" for the exam?+
Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.
Are these "Triangles" MCQs available with answers?+
Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to start practising, with instant scoring.
Is there negative marking in the "Triangles" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from Triangles (Class 9 Mathematics)?+
The questions that matter most test Congruent figures, Corresponding parts, SAS criterion, ASA criterion. This page shows 14 solved important MCQs with answers and explanations; all 90 questions on the chapter are available as timed quizzes once you sign in.
Is there an online quiz for Triangles?+
Yes — Class 9 Mathematics Triangles has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.