Triangles Class 9 Maths MCQs
Triangles is one of the most important chapters in CBSE Class 9 Maths because it builds the core foundation of geometry and logical reasoning. Many higher-level geometry concepts in future classes are directly connected to triangle properties, angle relationships, and congruency rules. This chapter is not only important for school exams but also helps students develop problem-solving skills step by step.
This page on Class 9 Maths MCQs OF Triangles with answers is created to help students practice important objective questions in a simple and exam-focused way. The triangles class 9 mcq collection includes questions based on types of triangles, congruency criteria, angle sum property, exterior angle theorem, and triangle inequalities. Students preparing for school exams, unit tests, and online assessments can use these MCQs for quick revision and concept improvement.
Many students understand the theory of triangles but become confused while solving diagram-based questions and theorem-related MCQs. Small mistakes in angle calculations or congruency conditions often lead to wrong answers. Regular practice of triangles mcq class 9 helps students improve accuracy, speed, and confidence while solving geometry questions.
What is Triangles MCQ Class 9?
Triangles MCQs for Class 9 Maths are multiple-choice questions designed to test a student’s understanding of triangle properties, angle relationships, and geometrical theorems. These questions are an important part of Class 9 Maths Chapter 7 MCQs with answers and are useful for both revision and exam preparation.
In these questions, students practice concepts like types of triangles, congruent triangles, angle sum property, exterior angle theorem, and inequalities in a triangle. Students also learn how geometrical rules are applied in solving real exam-level questions.
Regular practice of class 9 maths triangles mcqs with answers improves logical thinking, diagram understanding, and theorem application skills. It also helps students reduce confusion in geometry-based objective questions.
Important Terms in Triangles
| Term | Description | Example |
|---|---|---|
| Scalene Triangle | Triangle with all sides unequal | 5 cm, 6 cm, 7 cm |
| Isosceles Triangle | Triangle with two equal sides | 6 cm, 6 cm, 4 cm |
| Equilateral Triangle | Triangle with all sides equal | 5 cm, 5 cm, 5 cm |
| Congruent Triangles | Triangles having same shape and size | Identical triangles |
| Exterior Angle | Angle formed outside a triangle | Exterior angle at a vertex |
| Angle Sum Property | Sum of interior angles is 180 degrees | 60 + 70 + 50 |
This table is very useful for solving class 9 maths chapter 7 mcq online test questions quickly and correctly.
Triangles Important Tricks for MCQs of Class 9
Remember the Angle Sum Rule
The sum of all interior angles of a triangle is always 180 degrees. This rule is frequently used in MCQ questions.
Learn Congruency Criteria Properly
SSS, SAS, ASA, and RHS rules are very important for solving theorem-based questions quickly.
Focus on Exterior Angle Property
The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Observe Diagrams Carefully
Students often lose marks because they ignore angle markings and side labels in diagrams.
Compare Sides and Angles Smartly
The larger side of a triangle always faces the larger angle.
These tricks are very helpful while solving triangles class 9 mcq questions in exams and online tests.
Instructions for Students
- Read every question carefully before selecting an option
- Observe triangle diagrams properly before solving
- Avoid guessing answers without applying geometry rules
- Revise congruency criteria before attempting MCQs
- Practice angle-based questions regularly
- Solve NCERT examples for better concept clarity
- Attempt online tests to improve speed and accuracy
Q. In a triangle ABC, if AB = AC and ∠B = 70°, what is the measure of ∠C?
A) 40°
B) 70°
C) 110°
D) 140°
Answer: B
Explanation:
Since AB = AC, the triangle is isosceles and the angles opposite equal sides are equal. Therefore, ∠B = ∠C = 70°.
Q. Which of the following conditions is NOT sufficient to prove that two triangles are congruent?
A) SSS
B) SAS
C) ASS
D) ASA
Answer: C
Explanation:
ASS (Angle-Side-Side) is not a valid congruence criterion because it may produce two different triangles. SSS, SAS, and ASA are valid congruence rules.
Q. In ΔPQR, if ∠P = 60° and ∠Q = 80°, what is the measure of the exterior angle at vertex R?
A) 40°
B) 100°
C) 140°
D) 180°
Answer: C
Explanation:
The exterior angle of a triangle equals the sum of the two opposite interior angles. Therefore, exterior angle at R = 60° + 80° = 140°.
Q. If two sides of a triangle are 5 cm and 8 cm, which of the following cannot be the length of the third side?
A) 3 cm
B) 6 cm
C) 10 cm
D) 12 cm
Answer: D
Explanation: According to the triangle inequality theorem, the third side must be less than the sum and greater than the difference of the other two sides. Here, the third side must be between 3 cm and 13 cm, but it cannot be exactly 3 cm because the sum of two sides must be greater than the third side.
Q. In triangles ABC and DEF, AB = DE, BC = EF, and ∠B = ∠E. By which congruence rule are the triangles congruent?
A) SSS
B) SAS
C) ASA
D) RHS
Answer: B
Explanation:
Two sides and the included angle are equal in both triangles. Hence, the triangles are congruent by SAS congruence rule.
Q. Consider a right-angled triangle ABC, where ∠B = 90°. If AC is the hypotenuse, which statement is always true?
A) AB > AC
B) BC > AC
C) AC > AB and AC > BC
D) AB + BC < AC
Answer: C
Explanation:
In any right triangle, the hypotenuse is the longest side. Therefore, AC is greater than both AB and BC.
Q. In ΔABC, ∠A = 50°, ∠B = 60°, and ∠C = 70°, which side is the shortest?
A) AB
B) BC
C) AC
D) All sides are equal
Answer: B
Explanation:
The side opposite the smallest angle is the shortest side. Since ∠A = 50° is the smallest angle, the side opposite it, BC, is the shortest.
Q. Two triangles are congruent if two angles and the included side of one are equal to two angles and the included side of the other triangle. This is known as:
A) SSS
B) SAS
C) ASA
D) RHS
Answer: C
Explanation:
ASA congruence rule states that if two angles and the included side of one triangle are equal to the corresponding parts of another triangle, then the triangles are congruent.
Q. In ΔABC, if ∠A = 90° and AB = AC, what type of triangle is it?
A) Scalene triangle
B) Equilateral triangle
C) Isosceles right-angled triangle
D) Obtuse-angled triangle
Answer: C
Explanation:
Since AB = AC, the triangle is isosceles, and because one angle is 90°, it is an isosceles right-angled triangle.
Q. Which of the following is true for an equilateral triangle?
A) All sides are equal, and all angles are 60°
B) Two sides are equal
C) All angles are different
D) One angle is 90°
Answer: A
Explanation:
In an equilateral triangle, all three sides are equal and each angle measures 60°.
Q. If in ΔABC, AB = 7 cm, BC = 9 cm, and AC = 5 cm, which angle is the largest?
A) ∠A
B) ∠B
C) ∠C
D) Cannot be determined
Answer: A
Explanation:
The largest angle lies opposite the longest side. Since BC = 9 cm is the longest side, ∠A is the largest angle.
Q. In ΔABC and ΔPQR, if AB = PQ, BC = QR, and CA = RP, then the triangles are congruent by:
A) ASA
B) SAS
C) SSS
D) RHS
Answer: C
Explanation:
All three corresponding sides are equal, so the triangles are congruent by the SSS rule.
Q. If the sides of a triangle are in the ratio 2:3:4, what is the measure of the smallest angle?
A) 20°
B) 40°
C) 60°
D) 80°
Answer: A
Explanation:
The smallest angle lies opposite the smallest side. In this standard ratio-based triangle, the smallest angle is approximately 20°.
Q. Two right-angled triangles have equal hypotenuse and one corresponding side equal. By which rule are they congruent?
A) SSS
B) SAS
C) ASA
D) RHS
Answer: D
Explanation:
RHS congruence rule applies when the hypotenuse and one side of two right triangles are equal.
Q. If ∠B > ∠C in ΔABC, then which is true?
A) AC > AB
B) AB > AC
C) AC = AB
D) BC > AB
Answer: B
Explanation: The side opposite the greater angle is longer. Since ∠B > ∠C, side AC is greater than AB.
Q. The sum of the lengths of any two sides of a triangle is always:
A) Equal to the third side
B) Less than the third side
C) Greater than the third side
D) Half of the third side
Answer: C
Explanation:
This is the triangle inequality theorem. The sum of any two sides must always be greater than the third side.
Q. If the perimeter of an isosceles triangle is 30 cm and the unequal side is 10 cm, what is each equal side?
A) 5 cm
B) 10 cm
C) 15 cm
D) 20 cm
Answer: B
Explanation:
Let each equal side be x. Then 2x + 10 = 30. Therefore, x = 10 cm.
Q. If AB = AC and ∠A = 80°, what is the measure of ∠B?
A) 50°
B) 60°
C) 70°
D) 80°
Answer: A
Explanation:
In an isosceles triangle, base angles are equal. Remaining angle sum = 180° − 80° = 100°. Therefore, ∠B = ∠C = 50°.
Q. Which statement is true about the median of a triangle?
A) It is perpendicular to the opposite side
B) It bisects the angle
C) It connects a vertex to the midpoint of the opposite side
D) It divides the triangle into two congruent triangles
Answer: C
Explanation:
A median joins a vertex to the midpoint of the opposite side.
Q20. In two triangles ABC and DEF, AB = DE, ∠A = ∠D, and ∠B = ∠E. By which rule are the triangles congruent?
A) SSS
B) SAS
C) ASA
D) AAS
Answer: C
Explanation:
Two angles and the included side are equal, so the triangles are congruent by ASA rule.
Q. The exterior angle of a triangle is equal to the sum of:
A) One interior adjacent angle and one opposite angle
B) Two opposite interior angles
C) All three interior angles
D) Two adjacent interior angles
Answer: B
Explanation:
The exterior angle theorem states that an exterior angle equals the sum of the two opposite interior angles.
Q. If AB = 6 cm, BC = 8 cm, and AC = 10 cm, what type of triangle is it?
A) Acute-angled triangle
B) Obtuse-angled triangle
C) Right-angled triangle
D) Equilateral triangle
Answer: C
Explanation:
Since 6² + 8² = 10², the triangle satisfies Pythagoras theorem and is right-angled.
Q. If the angles of a triangle are (x + 10)°, (2x − 30)°, and (x + 20)°, find x.
A) 30
B) 40
C) 50
D) 60
Answer: B
Explanation:
Sum of angles of a triangle is 180°. Therefore, (x + 10) + (2x − 30) + (x + 20) = 180 ⇒ 4x = 160 ⇒ x = 40.
Q. In an isosceles triangle, the altitude drawn to the unequal side:
A) Always bisects the vertex angle
B) Sometimes true
C) Never true
D) True only for equilateral triangles
Answer: A
Explanation:
In an isosceles triangle, the altitude to the base also acts as a median and angle bisector.
Q. If ∠B corresponds to ∠Y in ΔABC and ΔXYZ, then:
A) ∠X
B) ∠Y
C) ∠Z
D) Cannot be determined
Answer: B
Explanation:
Corresponding angles are matched directly. Hence ∠B corresponds to ∠Y.
Q. In a triangle, if an exterior angle is 110° and one opposite interior angle is 50°, what is the other opposite interior angle?
A) 40°
B) 60°
C) 70°
D) 80°
Answer: B
Explanation:
Exterior angle = sum of opposite interior angles. Therefore, other angle = 110° − 50° = 60°.
Q. In ΔABC, AB = 5 cm, BC = 12 cm, and AC = 13 cm. What is the angle opposite the side of length 13 cm?
A) 30°
B) 60°
C) 90°
D) Cannot be determined
Answer: C
Explanation:
Since 5² + 12² = 13², the triangle is right-angled. The angle opposite the longest side (13 cm) is 90°.
Q. In ΔABC, if ∠A = 40° and ∠B = 70°, what is ∠C?
A) 50°
B) 60°
C) 70°
D) 80°
Answer: C
Explanation:
Sum of angles of a triangle is 180°. Therefore, ∠C = 180° − (40° + 70°) = 70°.
Q. If the angles of a triangle are all less than 90°, the triangle is called:
A) Right-angled triangle
B) Obtuse-angled triangle
C) Acute-angled triangle
D) Isosceles triangle
Answer: C
Explanation:
A triangle in which all angles are less than 90° is known as an acute-angled triangle.
Q. What is the maximum number of obtuse angles a triangle can have?
A) 0
B) 1
C) 2
D) 3
Answer: B
Explanation: A triangle can have only one obtuse angle because the sum of all angles is 180°. Two obtuse angles would exceed 180°.
Triangles MCQ Preparation Tips
Practice theorem-based questions regularly
Revise angle properties daily
Focus on congruency criteria carefully
Solve diagram-based questions step by step
Avoid calculation mistakes in angle sums
Attempt class 9 triangles online tests regularly
Use NCERT and CBSE-based questions for preparation
Analyze mistakes after every MCQ practice session
Regular practice helps students improve geometry understanding and increases confidence during exams.
Conclusion
Practicing Class 9 Maths Triangles MCQs with answers is one of the best ways to improve geometry concepts and theorem-based problem-solving skills. This chapter plays a very important role in strengthening logical thinking and preparing students for advanced mathematics topics in higher classes.
Regular MCQ practice helps students avoid common mistakes related to angles, congruency rules, and diagram interpretation. With proper revision and consistent practice, students can score better marks and solve geometry questions with more confidence in exams and online tests.