RD Sharma Solutions for Class 7 Maths Chapter 15 Properties of Triangles

Understanding triangles is a very important part of learning geometry in Class 7. Chapter 15 of the RD Sharma Mathematics book, Properties of Triangles, teaches us all about different types of triangles and their unique features. It explains the rules that apply to triangles, how they are formed, and how their sides and angles relate to each other. With the help of RD Sharma Solutions, students can understand these concepts in a step-by-step and easy-to-follow way.

Triangles are shapes that have three sides and three angles. Even though they may look simple, there are many interesting facts and rules about them. For example, the sum of the three angles in any triangle is always 180 degrees. This rule is true for every triangle, no matter what shape or size it is. In this chapter, students will also learn about different types of triangles based on their sides and angles—like equilateral triangles (all sides are equal), isosceles triangles (two sides are equal), and scalene triangles (no sides are equal).

Do Check: RD Sharma Solutions for Class 7 Maths

RD Sharma Solutions help students by offering clear explanations, solved examples, and practice questions for every topic. The solutions follow the latest CBSE curriculum and are designed in a way that makes learning easy and enjoyable. Each solution is written in simple steps, so students can understand how to approach and solve different types of triangle-related problems. This also helps them build a strong foundation in geometry, which is useful not just in exams but also in real-life problem-solving.

Another important topic covered in this chapter is the Pythagoras Theorem, which applies to right-angled triangles. This is one of the most famous rules in mathematics, and it is used in many practical situations. RD Sharma Solutions explain this theorem with simple examples and pictures to make it easier for students to understand.

In short, RD Sharma Solutions for Class 7 Chapter 15 are a great way to revise the chapter and gain confidence in solving problems. Whether you are preparing for exams or simply want to strengthen your understanding of triangles, these solutions are the perfect guide to help you succeed.

Download RD Sharma Solutions for Class 7 Maths Chapter 15 Properties of Triangles PDF Here

RD Sharma Class 7 Chapter 15 PDF includes detailed solutions, examples, and extra questions to help you master real numbers and other topics. Click here to download the RD Sharma Class 7 Chapter 15 PDF.

Access Answers to RD Sharma Solutions for Class 7 Maths Chapter 15 Properties of Triangles

In this chapter, students will learn about decimals and how to perform basic operations with them. The solutions provided here are detailed and easy to follow, helping students understand each concept thoroughly.

Q1. What is the difference between a triangle and a triangular region?

Triangle: A triangle is a flat shape made by joining three straight line segments that do not lie on the same line.

Triangular region: A triangular region includes not only the triangle but also everything inside it.

Q2. Fill in the blanks with the correct word or symbol to make the statement true:

(i) A triangle has three sides.

(ii) A triangle has three vertices.

(iii) A triangle has three angles.

(iv) A triangle has six parts.

(v) A triangle with all sides of different lengths is called a scalene triangle.

(vi) A triangle with two equal sides is called an isosceles triangle.

(vii) A triangle with all sides equal is called an equilateral triangle.

(viii) A triangle with one right angle is called a right triangle.

(ix) A triangle where all angles are less than 90° is called an acute triangle.

(x) A triangle with one angle more than 90° is called an obtuse triangle.

Q3. Say whether the following statements are True (T) or False (F):

(i) A triangle has three sides. — True

(ii) A triangle can have four corners. — False

(iii) Any three line segments can make a triangle. — False

(iv) The inside part of a triangle includes the corners. — False

(v) A triangular region includes the triangle and the space inside it. — True

(vi) A triangle’s corners lie in a straight line. — False

(vii) An equilateral triangle is also an isosceles triangle. — True

(viii) Every right triangle is scalene. — False

(ix) Every acute triangle is equilateral. — False

(x) No isosceles triangle is obtuse. — False

Q4. Two angles of a triangle measure 150° and 30°. What is the third angle?

Given: Two angles = 150° and 30°

Total sum of angles in a triangle = 180°

150° + 30° + x = 180°

x = 180° − 180° = 0°

(Note: This triangle is not possible as sum exceeds 180°)

Q5. One angle of a triangle is 130° and the other two are equal. Find those angles.

Let each equal angle be x

130° + x + x = 180°

2x = 180° − 130° = 50°

x = 25°

The other two angles are 25° each.

Q6. All three angles of a triangle are equal. Find each angle.

Let each angle be x

3x = 180°

x = 60°

Each angle measures 60°.

Q7. The angles of a triangle are in the ratio 1:2:3. Find the angles.

Let the angles be x, 2x, 3x

x + 2x + 3x = 180°

6x = 180° → x = 30°

So the angles are 30°, 60°, 90°.

Q8. The triangle has angles (x−40)°, (x−20)°, and (½x−10)°. Find x.

(x − 40) + (x − 20) + (½x − 10) = 180

2.5x − 70 = 180

2.5x = 250

x = 100

The value of x is 100°.

Q9. The triangle’s angles are in increasing order with a 10° gap. What are the angles?

Let the smallest angle be x

Next: x + 10°, Last: x + 20°

x + x + 10 + x + 20 = 180 → 3x + 30 = 180

x = 50

Angles are 50°, 60°, 70°.

Q10. Two triangle angles are the same. Third is 30° more than each. Find all angles.

Let equal angles be x

Third angle = x + 30

x + x + x + 30 = 180 → 3x + 30 = 180

x = 50

Angles are 50°, 50°, 80°.

Q11. One angle of a triangle equals the sum of the other two. Prove it's a right triangle.

Let the angles be x, y, z

Suppose x = y + z

Total = x + y + z = 180

But x = y + z → So, x + x = 180 → 2x = 180 → x = 90°

So, if one angle is the sum of the other two, it is 90°, which means the triangle is a right triangle.