Chapter 7 · Class 9 CBSE · MCQ Test
Triangles MCQ Test — Class 9 CBSE
Practice 10 multiple-choice questions with instant answer reveal and explanations.
Triangles — MCQ Questions
1Which of the following statements correctly defines congruent figures?
Show Answer+
Answer: C) Figures that have exactly the same shape and the same size.
Hint: Think about what 'congruent' means in everyday language, applied to geometric shapes.
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.
2If ΔPQR ≅ ΔXYZ, which of the following statements is NOT necessarily true?
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.
Solution:
When two triangles are congruent, their corresponding parts (sides and angles) are equal (CPCTC).
From the congruence statement ΔPQR ≅ ΔXYZ, the corresponding parts are: PQ ↔ XY, QR ↔ YZ, PR ↔ XZ, ∠P ↔ ∠X, ∠Q ↔ ∠Y, ∠R ↔ ∠Z.
Therefore, PQ = XY, QR = YZ, and ∠P = ∠X are all necessarily true. However, PR corresponds to XZ, not YZ. So, PR = YZ is not necessarily true.
3To 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?
Show Answer+
Answer: B) AC = DF
Hint: The SSS criterion requires all three pairs of corresponding sides to be equal.
Solution:
The SSS congruence criterion states that if three sides of one triangle are equal to three corresponding sides of another triangle, then the triangles are congruent.
Given AB = DE and BC = EF, the third pair of corresponding sides that must be equal is AC and DF.
4Rohan 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?
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.
Solution:
The SAS congruence criterion requires two sides and the *included angle* (the angle formed between those two sides) of one triangle to be equal to two sides and the *included angle* of another triangle.
In ΔPQR, for sides PQ and PR, the included angle is ∠P. Rohan used ∠Q, which is not included between PQ and PR.
5Consider two triangles, ΔABC and ΔXYZ. If it is given that ∠A = ∠X, AB = XY, and ∠B = ∠Y, which congruence criterion can be used to prove ΔABC ≅ ΔXYZ?
Show Answer+
Answer: C) ASA
Hint: Look at the sequence of the given equal parts: Angle, Side, Angle. Is the side included between the two angles?
Solution:
We are given two angles and a side: ∠A = ∠X, AB = XY, and ∠B = ∠Y.
The side AB is *included* between angles ∠A and ∠B in ΔABC. Similarly, XY is included between ∠X and ∠Y in ΔXYZ.
Since two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, the ASA (Angle-Side-Angle) congruence criterion applies.
6For two right-angled triangles to be congruent by the RHS (Right angle - Hypotenuse - Side) congruence criterion, which of the following is a mandatory condition?
Show Answer+
Answer: C) Their hypotenuses must be equal, and one pair of corresponding sides (other than the hypotenuse) must be equal.
Hint: RHS specifically applies to *right-angled* triangles and requires equality of the hypotenuse and one other side.
Solution:
The RHS congruence criterion applies only to right-angled triangles.
It states that if the hypotenuse and one side of a right-angled triangle are equal to the hypotenuse and one side of another right-angled triangle, then the two triangles are congruent.
7In an isosceles triangle ΔABC, if AB = AC and ∠B = 65°, what is the measure of ∠C?
Show Answer+
Answer: B) 65°
Hint: Remember the property of isosceles triangles: angles opposite to equal sides are equal.
Solution:
Given that ΔABC is an isosceles triangle with AB = AC.
The property of isosceles triangles states that the angles opposite to the equal sides are equal.
Therefore, the angle opposite to side AC (which is ∠B) must be equal to the angle opposite to side AB (which is ∠C). So, ∠C = ∠B.
Since ∠B = 65°, then ∠C must also be 65°.
8In ΔDEF, if ∠D = ∠F, which of the following statements must be true?
Show Answer+
Answer: C) DE = EF
Hint: This is the converse of the property you used in the previous question. If angles are equal, what about the sides opposite to them?
Solution:
The property states that sides opposite to equal angles of a triangle are equal.
Given ∠D = ∠F. The side opposite to ∠D is EF, and the side opposite to ∠F is DE.
Therefore, if ∠D = ∠F, then DE must be equal to EF.
9Consider two triangles, ΔPQR and ΔLMN. If we are given that PQ = LM, ∠Q = ∠M, and QR = MN, which congruence criterion can be used to prove ΔPQR ≅ ΔLMN?
Show Answer+
Answer: B) SAS
Hint: Identify the type of parts given (Side, Angle, Side) and their arrangement. Is the angle *between* the two sides?
Solution:
We are given: PQ = LM (Side), ∠Q = ∠M (Angle), and QR = MN (Side).
In ΔPQR, the angle ∠Q is *included* between the sides PQ and QR. Similarly, in ΔLMN, the angle ∠M is *included* between the sides LM and MN.
Since two sides and the included angle of ΔPQR are equal to two sides and the included angle of ΔLMN, the SAS (Side-Angle-Side) congruence criterion applies.
10If in two triangles, ΔABC and ΔDEF, it is given that AB = DE, BC = EF, and ∠A = ∠D, can we always conclude that ΔABC ≅ ΔDEF?
Show Answer+
Answer: C) No, because SSA is not a valid congruence criterion.
Hint: This arrangement of Side-Side-Angle (SSA) is often a trick question. Think if this combination uniquely determines a triangle.
Solution:
The given information is two sides (AB = DE, BC = EF) and a non-included angle (∠A = ∠D). This configuration is known as SSA (Side-Side-Angle).
SSA is not a valid congruence criterion. Unlike SSS, SAS, ASA, and RHS, the SSA condition does not guarantee congruence because it can lead to an ambiguous case where two different triangles can be formed with the given measurements.
Therefore, we cannot always conclude that the triangles are congruent.
Want more questions?
Practice 60+ questions with AI-powered doubt clearing and step-by-step solutions.
Tips for Triangles MCQs
- 1Read each question carefully and identify what is being asked before looking at the options.
- 2Try to solve the problem mentally or on paper first, then match your answer with the options.
- 3Use elimination — rule out clearly wrong options to improve your chances even when unsure.
- 4Check units, signs, and edge cases — these are common traps in Triangles MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
Master Triangles on SparkEd
Go beyond MCQs. Practice at three difficulty levels with instant feedback, solutions, and an AI coach to clear every doubt.
Start PractisingSparkEd Maths offers free MCQ tests for Class 1-10 across 7 education boards. All questions are aligned to the 2025-26 syllabus with step-by-step solutions and AI-powered doubt clearing.