Triangles Class 9 Important Questions Free PDF Download

Triangles are one of the most significant topics in Class 9 Mathematics, forming the foundation for advanced geometry. Chapter 7, "Triangles," focuses on various properties, theorems, and criteria for congruence that help understand the geometry of this three-sided polygon. Mastering this chapter enhances problem-solving skills and logical thinking, essential for board exams. In this blog, we cover a collection of Triangles Class 9 Important Questions based on key concepts like the Pythagoras Theorem, congruence criteria (SSS, SAS, ASA, RHS), and triangle inequality property. These questions will help students build confidence, practice efficiently, and prepare effectively for their CBSE exams.

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In the table given below, we have provided the links to Class 9 Maths Chapter 7 Extra Questions with Solutions PDFs. You can download them without having to share any login info.

Chapter 7 Triangles Important Questions

In the given figure, the isosceles triangle ABC ≅ EAD. The point E is equidistant from both A and B

1. What is the value of x?

Solutions: 

Since △ABC≅△EAD, all corresponding angles and sides of the triangles are equal. Therefore:

∠ABC=∠EAD and ∠CAB=∠DEA

Since △ABC is isosceles, let ∠ABC=∠CAB=x (base angles of △ABC).

The sum of angles in △ABC  is 180°

x+x+80°=180°

2x=100°

⇒x=50°‍

2. What is the value of y?

Solutions: 

△ABC is isosceles,with ∠ABC=∠CAB=50°

Since △ABC≅△EAD

Corresponding angles are equal, so ∠EAD=∠ABC=50°

∠DEA=∠CAB=50°

In △ADE: The sum of the angles in △ADE is 180°

∠DEA+∠EAD+∠ADE=180°

Substituting the known values:

50°+50°+y=180°

y=180°−100°

=80°

 3. What is the value of ∠BDC?

Solutions:

△ABC is isosceles, 

so ∠ABC=∠CAB=50°

∠BCA= 80° (given).

△ABC≅△EAD

△EBD is isosceles,as E is equidistant from A and B, making EA=EB

In quadrilateral ABCD, ∠BDC is an external angle to △BCD. Using the exterior angle theorem:

∠BDC=∠ABC+∠BCA

Substituting the known values:

∠BDC=50°+80°

=130°

Chapter 7 Triangles Important Questions: Concepts

A triangle is a closed figure formed by three line segments. It's one of the most fundamental shapes in geometry. In Class 9, we study its properties, theorems, and problems.

Key Concepts

Types of Triangles: Based on sides (scalene, isosceles, equilateral) and angles (acute, obtuse, right-angled).

Congruence of Triangles: Two triangles are congruent if they have the same shape and size. Congruence criteria include:

• SSS (Side-Side-Side)
• SAS (Side-Angle-Side)
• ASA (Angle-Side-Angle)
• AAS (Angle-Angle-Side)
• RHS (Right-Angle-Hypotenuse-Side)

Triangle Inequality Property: The sum of any two sides of a triangle is always greater than the third side.

Pythagoras Theorem: In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Important Theorems

1. Angle Sum Property: The sum of the three angles of a triangle is 180°.
2. Midpoint Theorem: A line drawn from the midpoint of one side of a triangle parallel to another side bisects the third side.
3. Exterior Angle Property: The measure of the exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Sample Questions

• Prove the congruence of two triangles using any suitable criterion.
• Find the unknown angles of a triangle using the angle sum property.
• Verify the Pythagoras theorem in a given triangle.
• Solve problems related to the triangle inequality property.
• Prove that a line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.

Chapter 7 Triangles Important Questions: Why

Chapter 7 on Triangles is crucial for students as it forms the basis of many geometric concepts in higher grades. Understanding triangles not only strengthens your foundation in geometry but also enhances logical reasoning and problem-solving skills. 

Foundation for Geometry: Triangles form the basis of many geometric concepts in higher grades.

Key Theorems: Important theorems like Pythagoras Theorem, Triangle Congruence, and Angle-Sum Property are essential to learn.

Exam Relevance: These concepts frequently appear in CBSE exams and other competitive tests.

Improves Problem-Solving Skills: Practicing important questions helps sharpen logical thinking and problem-solving abilities.

Boosts Confidence: Regular practice increases accuracy and builds confidence in solving complex problems.

Logical Reasoning: Mastering triangle-related questions strengthens logical reasoning skills needed for advanced mathematics.

The importance of practising triangles class 9 important questions with solutions in this chapter lies in mastering fundamental theorems like the Pythagoras Theorem, Triangle Congruence, and the Angle-Sum Property. These concepts appear frequently in exams and competitive tests. By focusing on important questions, students can improve their accuracy, develop a deeper understanding, and boost their confidence in tackling complex problems.

Chapter 7 Triangles Important Questions: How

Understand Key Concepts: Start by thoroughly understanding the basic properties of triangles, such as types (scalene, isosceles, equilateral) and important theorems (Angle-Sum Property, Triangle Inequality, etc.).

Learn Congruence Criteria: Focus on different congruence rules (SSS, SAS, ASA, RHS) and practice applying them to determine if two triangles are congruent.

Practice Theorems and Proofs: Work on proving theorems like the Midpoint Theorem and Exterior Angle Theorem, as these often appear in exam questions.

Work on Triangle Inequality: Practice problems involving the sum of two sides being greater than the third side, a key part of triangle-related questions.

Solve Real-Life Problems: Apply concepts to real-life problems and diagrams, which will help in understanding how to solve questions logically and step by step.

Solve Previous Year Questions: Reviewing previous exam papers helps understand the types of questions asked and allows you to practice time management during exams.

Seek Clarification: If certain concepts or questions are challenging, seek clarification from teachers, peers, or study resources to strengthen your understanding.

We hope that you practice the above Class 9 Maths Chapter 7 Important Questions and achieve your dream marks.

All the Best!