≅ CPCT SAS · ASA · AAS SSS · RHS SSA ✗ NOT valid AAA → similar only Isosceles: opp. equal sides ⟹ equal angles
△≅△
Chapter 7  ·  Class IX Mathematics  ·  MCQ Practice

MCQ Practice Arena

Triangles

Congruence Rules and Inequalities — Prove Fast, Score Full

📋 50 MCQs ⭐ 28 PYQs ⏱ 75 sec/Q
🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs
16Easy
22Medium
12Hard
28PYQs
75 secAvg Time/Q
8Topics
Easy 32% Medium 44% Hard 24%

Why Practise These MCQs?

CBSE Class IXNTSEState BoardsOlympiad

Triangles is the highest-weight geometry chapter in Class IX — congruence criteria (SAS, ASA, AAS, SSS, RHS) appear in both MCQ and proof formats. CBSE Boards include proof questions (5 marks) and direct MCQs (1 mark) from this chapter every year. NTSE uses congruence chains and inequality reasoning. The key skill is identifying which congruence rule applies — practice this until it is automatic.

Topic-wise MCQ Breakdown

Congruence of Triangles (Concept)5 Q
SAS Congruence Rule8 Q
ASA Congruence Rule8 Q
AAS Congruence Rule6 Q
SSS Congruence Rule7 Q
RHS Congruence Rule6 Q
Properties of Isosceles Triangles6 Q
Triangle Inequalities4 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$\text{SAS: two sides + included angle}$
$\text{ASA: two angles + included side}$
$\text{AAS: two angles + non-included side}$
$\text{SSS: all three sides equal}$
$\text{RHS: right angle + hypotenuse + one side}$
$\text{Isosceles: angles opp. equal sides are equal}$
$\text{Sum of any two sides} > \text{third side}$

MCQ Solving Strategy

For congruence MCQs, list the given information side-by-side for both triangles — this makes the applicable rule obvious. SAS requires the angle to be BETWEEN the two sides (included). ASA requires the side to be BETWEEN the two angles. If you have a right angle plus hypotenuse plus one side, use RHS directly. For isosceles triangle MCQs, always draw the triangle and mark the equal sides first.

⚠ Common Traps & Errors

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Identify congruence rule from given data, state CPCT, isosceles angle properties

② Medium

Find missing sides/angles using congruence, two-step proofs

③ Hard

Triangle inequalities, multi-triangle congruence chains, angle bisector theorems

★ PYQ

CBSE — state rule + prove; NTSE — congruence in complex diagrams

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 📘✔️ Exercises Step-by-step NCERT solutions ✔️❌ True / False Concept-based True & False ➡ Next Chapter Quadrilaterals
🎯 Knowledge Check

Maths — TRIANGLES

50 Questions Class 9 MCQs
1
Two figures are said to be congruent, if they have
2
Two triangles are congruent if their corresponding sides and angles are
3
Which of the following is a criterion for congruence of triangles?
4
The symbol for congruence is
5
If two sides and included angle of one triangle are equal to the corresponding parts of another, the triangles are congruent by
6
Which of these is not a criterion for congruence?
7
If all sides of one triangle are equal to all sides of another, then triangles are congruent by
8
In ?ABC and ?PQR, if AB = PQ, BC = QR and AC = PR, then
9
ASA stands for
10
RHS criterion applies to
11
Two right triangles are congruent if hypotenuse and one side are equal. This is called
12
The word “congruent” comes from
13
In ?ABC ? ?DEF, the vertex corresponding to A is
14
If two angles of one triangle are equal to two angles of another, then third angles are
15
If ?ABC ? ?PQR, then which of these is true?
16
If two sides of a triangle are equal, then
17
In an isosceles triangle, the equal sides are called
18
The line joining vertex to midpoint of opposite side is called
19
An altitude of a triangle is
20
In an isosceles triangle, the altitude from vertex bisects
21
In a scalene triangle
22
Equilateral triangle is also
23
The measure of each angle in an equilateral triangle is
24
The sum of angles in a triangle is
25
If two triangles are congruent, then their areas are
26
If ?ABC ? ?DEF, then ?A = ?
27
If two angles and one included side of one triangle are equal to corresponding parts of another, triangles are congruent by
28
Two triangles are congruent if their three sides are equal. This is
29
If two triangles are congruent, then their corresponding parts are
30
CPCT stands for
31
A triangle with sides 3 cm, 4 cm, and 5 cm is
32
The triangle with angles 50°, 60°, 70° is
33
If a triangle has two equal sides, it is called
34
If all angles of a triangle are equal, the triangle is
35
The perpendicular bisectors of sides of a triangle intersect at
36
The medians of a triangle meet at
37
The angle bisectors of a triangle intersect at
38
The altitudes of a triangle meet at
39
In an equilateral triangle, all centres coincide.
40
The perpendicular drawn from the vertex of an isosceles triangle bisects
41
Two triangles are said to be similar if their
42
The ratio of areas of two similar triangles is equal to
43
In a right triangle, if one acute angle is 30°, the other is
44
A triangle can be constructed if sum of any two sides is
45
If two sides of a triangle are unequal, the larger angle lies
46
The line segment joining midpoints of two sides of a triangle is
47
In ?ABC, D and E are midpoints of AB and AC, then DE = ?
48
Which theorem states “Angles opposite to equal sides are equal”?
49
In a triangle, the side opposite the smallest angle is
50
The sum of lengths of any two sides of a triangle is always
📚
ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025
Sharing this chapter
Class 9 Maths Triangles 50 MCQs with Answers
Class 9 Maths Triangles 50 MCQs with Answers — Complete Notes & Solutions · academia-aeternum.com
Understanding Triangles is a vital part of Class 9 Mathematics, as it lays the foundation for higher geometry concepts in later classes and competitive exams. This collection of 50 Multiple Choice Questions (MCQs) from NCERT Chapter 7 – Triangles has been carefully curated to help students revise, practice, and master all key topics such as congruence of triangles, properties of isosceles and equilateral triangles, midpoint theorem, triangle inequalities, and RHS criterion. Each question is…
🎓 Class 9 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
Share on
WhatsApp
Telegram
X / Twitter
Facebook
Instagram
Threads
Pinterest
LinkedIn
Quora
Discord
Reddit
Email
academia-aeternum.com/class-9/mathematics/triangles/mcqs/ Copy link
💡
Exam tip: Sharing chapter notes with your study group creates a reinforcement loop. Teaching a concept is the fastest path to mastering it.

Frequently Asked Questions

A triangle is a polygon with three sides, three vertices, and three angles.

Equilateral (all sides equal), Isosceles (two sides equal), Scalene (all sides different).

Acute (all angles < 90°), Right (one angle = 90°), Obtuse (one angle > 90°).

The sum of all interior angles of a triangle is always 180 degrees.

The exterior angle of a triangle equals the sum of the two opposite interior angles.

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Triangles with equal corresponding sides and angles are congruent and can be superimposed on each other.

\(\text{SSS (Side-Side-Side),}\\ \text{SAS (Side-Angle-Side),}\\ \text{ASA (Angle-Side-Angle),}\\ \text{AAS (Angle-Angle-Side),}\\\small\text{RHS (Right angle-Hypotenuse-Side).}\)

Triangles with all three sides equal are congruent.

If two sides and the included angle are equal, the triangles are congruent.

If two angles and the included side are equal, the triangles are congruent.

For right triangles, if the hypotenuse and one side are equal, the triangles are congruent.

Area = (1/2) × base × height

By adding the lengths of all three sides. Perimeter = a + b + c

A line segment drawn from a vertex to the midpoint of the opposite side.

Recent Posts

    --:-- ⏱ Time
    ⚡ Progress 0 / 50 answered

    TRIANGLES — Learning Resources

    📄 Detailed Notes
    ✔️ True / False
    📌 Exercise
    📝 Exercises
    Exercise-7.1 Exercise-7.2 Exercise-7.3
    📚
    ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025
    Sharing this chapter
    Class 9 Maths Triangles 50 MCQs with Answers
    Class 9 Maths Triangles 50 MCQs with Answers — Complete Notes & Solutions · academia-aeternum.com
    Understanding Triangles is a vital part of Class 9 Mathematics, as it lays the foundation for higher geometry concepts in later classes and competitive exams. This collection of 50 Multiple Choice Questions (MCQs) from NCERT Chapter 7 – Triangles has been carefully curated to help students revise, practice, and master all key topics such as congruence of triangles, properties of isosceles and equilateral triangles, midpoint theorem, triangle inequalities, and RHS criterion. Each question is…
    🎓 Class 9 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
    Share on
    WhatsApp
    Telegram
    X / Twitter
    Facebook
    Instagram
    Threads
    Pinterest
    LinkedIn
    Quora
    Discord
    Reddit
    Email
    academia-aeternum.com/class-9/mathematics/triangles/mcqs/ Copy link
    💡
    Exam tip: Sharing chapter notes with your study group creates a reinforcement loop. Teaching a concept is the fastest path to mastering it.

    Get in Touch

    Let's Connect

    Questions, feedback, or suggestions?
    We'd love to hear from you.