RD Sharma Solutions Class 6 Maths Chapter 12 Triangles - Free PDF Download

Think about connecting any three dots on a piece of paper with straight lines. What shape do you usually get? A triangle! These shapes are made of three lines and have three corners, which we call points. In Chapter 12 of your RD Sharma Class 6 Maths book, we're going to learn and practice all about these cool triangle shapes. We'll practice that there are different kinds of triangles, some with equal sides, some with different angles, and some with a mix of both. We'll also discover some special things about triangles that always hold true. 

RD Sharma Solutions Class 6 Maths Chapter 12 Triangles

The RD Sharma Solutions for Class 6 Maths Chapter 12 – Triangles offer well-explained answers to all textbook questions, helping students understand the basic properties and types of triangles effectively. These solutions are an ideal resource for doubt clearing and quick revision before exams. Whether it's understanding scalene, isosceles, or equilateral triangles, or learning about angles and sides, this chapter builds a strong foundation in geometry.

Aligned with the latest CBSE syllabus for 2025-26, the RD Sharma Class 6 Triangles chapter includes step-by-step explanations, solved examples, and practice questions to ensure complete concept clarity. Students can also explore extra questions to strengthen their grasp of the topic and prepare confidently for their tests.

Download RD Sharma Class 6 Chapter 12 PDF with Solutions

Gain access to detailed and easy-to-understand solutions for all triangle-related problems and improve your geometry skills with confidence.

Downloading the RD Sharma Class 6 Chapter 12 PDF with solutions allows students to:

• Access expertly solved problems that clarify each concept in detail.
• Practice a variety of questions, including objective types, to enhance exam readiness.
• Learn tips, tricks, and stepwise explanations that improve both speed and accuracy in solving mathematical problems.
• Strengthen conceptual learning by applying formulas and logical reasoning to different types of triangle-related questions

Don't Miss: PDF for All Chapters

RD Sharma Solutions Class 6 Maths Chapter 12 Triangles

 1. Can a triangle have angles measuring 100°, 40°, and 50°? Justify your answer.
Sum = 100 + 40 + 50 = 190° > 180°
So, it's not possible.
Ans: No, triangle angle sum cannot exceed 180°.

2. If the exterior angle of a triangle is 110°, and one interior opposite angle is 45°, find the other opposite interior angle.
Exterior angle = sum of two opposite interior angles
110 = 45 + x → x = 65°
Ans: 65°

3. Find the type of triangle whose angles are 90°, 45°, and 45°.
Two angles equal → Isosceles
One 90° → Right-angled
Ans: Right-angled isosceles triangle

4. The perimeter of an equilateral triangle is 24 cm. Find the length of each side.
3 equal sides → 24 ÷ 3 = 8 cm
Ans: 8 cm

5. The sum of two angles of a triangle is 150°. What is the third angle? What type of triangle can it be?
Third angle = 180 − 150 = 30°
One angle < 90°, so triangle is acute-angled or scalene
Ans: 30°, triangle can be acute or scalene

6. Prove that a triangle cannot have more than one obtuse angle. Justify using angle sum property.
Let’s assume a triangle has two obtuse angles.

An obtuse angle is greater than 90°.

So two obtuse angles would sum to more than 180°, e.g., 100° + 95° = 195°.

But the sum of all angles in a triangle is always 180°, which contradicts our assumption.

Hence, a triangle can have at most one obtuse angle.

7. A triangular garden has two equal-length sides of 13 cm each, and the third side (the base) measures 10 cm. A gardener wants to install a decorative pole exactly at the center of the base and extend it straight up to meet the top vertex. What will be the height of the pole from the base to the top of the triangle?

This is an isosceles triangle, and the pole represents the height drawn from the top vertex perpendicular to the base.

Let’s split the triangle into two equal right-angled triangles.

Half of the base = 10 ÷ 2 = 5 cm

Hypotenuse (equal side) = 13 cm

8.  A triangle has two angles equal and the third angle is 20° less than twice one of the equal angles. Find all the angles of the triangle.
Let each equal angle be x
Then the third angle = 2x − 20
Using angle sum: x + x + (2x − 20) = 180
4x − 20 = 180
4x = 200 → x = 50
Third angle = 2×50 − 20 = 80

Angles: 50°, 50°, 80°

9. In triangle ABC, ∠A = 90°, AB = 6 cm, and AC = 8 cm. Find the length of side BC. What kind of triangle is it?
Using Pythagoras Theorem:
AB² + AC² = BC²
6² + 8² = BC² → 36 + 64 = 100
BC² = 100 → BC = √100 = 10 cm

Triangle ABC is a right-angled triangle (with sides forming a Pythagorean triplet: 6-8-10)

10. Can an obtuse-angled triangle be equilateral? Explain.
Answer: No
Explanation: An equilateral triangle has all angles = 60°, but an obtuse triangle must have one angle > 90°. So, they are mutually exclusive.

11. The ratio of angles of trinage is 2:3:4. Find all three angles and the type of triangle.
Answer:
Sum = 180°
Let angles be 2x, 3x, 4x → 2x + 3x + 4x = 9x = 180° → x = 20°
Angles = 40°, 60°, 80°
Type: Scalene and Acute-angled

12. Can a triangle have side lengths in the ratio 3:4:8? Why or why not?
Answer: No
Explanation: 3 + 4 = 7 < 8 → violates triangle inequality rule

13. What is the sum of exterior angles of any triangle, and why?
Answer: 360°
Explanation: At each vertex, exterior angle = 180° - interior angle. Total = 3 × 180° - 180° (sum of interior angles) = 360°

14. Identify whether the triangle with sides 9 cm, 40 cm, and 41 cm is a right triangle.
Answer:
=81+1600=1681 and (41)^2=1681

Since both are equal, it satisfies the Pythagorean Theorem.
So, the triangle is a right-angled triangle.

15. What is the minimum and maximum number of lines of symmetry a triangle can have?
Answer:

Minimum: 0 (Scalene triangle)

Maximum: 3 (Equilateral triangle)

16. Can a triangle have all three angles as right angles? Justify your answer
Answer:
Each right angle = 90°
Three right angles = 270° > 180°
Violates triangle sum property ⇒ Not possible