Triangles are one of the most important shapes in geometry. You’ll see triangles everywhere—in road signs, buildings, bridges, and even in nature. In Class 7 Maths Chapter 15, "Properties of Triangles," students learn the special features that make triangles unique. This chapter helps you understand how the sides and angles of a triangle are connected, and how these rules help us solve many mathematical problems.
RD Sharma's solutions for this chapter are designed in a simple, step-by-step way to help students learn quickly and easily. These solutions explain all the key concepts in clear language, with examples and proper working steps. Whether it’s the angle sum property of a triangle or the triangle inequality rule, every topic is covered in a way that makes it easy to understand. You will also learn about different types of triangles based on sides (like equilateral, isosceles, and scalene) and angles (like acute, right, and obtuse). RD Sharma’s exercises give you practice in using these properties to solve real problems. These questions not only help you prepare for exams but also build a strong foundation for future geometry chapters.
Do Check: RD Sharma Solutions for Class 7 Maths
If you ever find it confusing to remember rules or apply formulas, these RD Sharma solutions will guide you with simple explanations and tips. They make learning fun and reduce the fear of maths. By regularly solving these exercises, you’ll become confident in handling triangle-related questions. So, if you want to score well and really understand how triangles work, RD Sharma Solutions for Class 7 Chapter 15 is the perfect companion for you.
Download RD Sharma Solutions for Class 7 Maths Chapter 15 Properties of Triangles PDF Here
You can easily download the RD Sharma Solutions for Class 7 Maths Chapter 15 – Properties of Triangles PDF from here. This PDF has all the solved questions from the chapter, explained in simple steps. It helps you understand important concepts like the types of triangles, the angle sum property, and the triangle inequality rule. The solutions are written in an easy-to-follow way so that you can study at your own pace. Whether you want to revise before exams or practice daily, this PDF is perfect for quick and clear learning
Access Answers to RD Sharma Solutions for Class 7 Maths Chapter 15 Properties of Triangles
Q1. How is a triangle different from a triangular region?
Answer: A triangle is a closed shape formed by joining three straight lines. These lines meet at three points, forming three corners or angles. The triangle only includes the boundary (the three sides). A triangular region includes the triangle and everything inside it. That means it covers the full space within the triangle, not just the lines.
Q2. Complete the blanks with suitable words or symbols:
(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 sides equal is called an isosceles triangle.
(vii) A triangle with all sides the same is called an equilateral triangle.
(viii) A triangle with one angle equal to 90° is a right triangle.
(ix) A triangle with all angles less than 90° is an acute triangle.
(x) A triangle with one angle more than 90° is an obtuse triangle.
Q3. Mark each statement as 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 form 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. — True
(vi) The corners of a triangle lie in a straight line. — False
(vii) An equilateral triangle is also an isosceles triangle. — True
(viii) All right triangles are scalene. — False
(ix) Every acute triangle is equilateral. — False
(x) No isosceles triangle can be obtuse. — False
Q4. Two angles of a triangle are 150° and 30°. What is the third angle?
Answer:
Sum of angles in a triangle = 180°
Given angles = 150° and 30°
Total = 150° + 30° = 180°
The third angle becomes 0°, which is not possible. So, such a triangle cannot exist.
Q5. One angle is 130°, and the other two are equal. Find all angles.
Answer:
Let each equal angle be x.
Equation: 130° + x + x = 180° → 2x = 50° → x = 25°
So, the angles are: 130°, 25°, and 25°.
Q6. All angles are equal in a triangle. What is the measure of each?
Answer:
Let each angle be x.
3x = 180° → x = 60°
Each angle = 60°.
Q7. Angles are in the ratio 1:2:3. Find the angles.
Answer:
Let angles be x, 2x, 3x.
x + 2x + 3x = 180° → 6x = 180° → x = 30°
Angles are: 30°, 60°, and 90°.
Q8. Find x if angles are (x−40)°, (x−20)°, and (½x−10)°.
Answer:
Add: (x−40) + (x−20) + (½x−10) = 180
→ 2.5x − 70 = 180 → 2.5x = 250 → x = 100°
Q9. A triangle has angles increasing by 10°. What are the angles?
Answer:
Let first angle be x. Others are x+10 and x+20.
x + x+10 + x+20 = 180 → 3x + 30 = 180 → x = 50
Angles are: 50°, 60°, 70°.
Q10. Two angles are the same. The third is 30° more than the equal ones. Find all angles.
Answer:
Let equal angles be x. Then third angle = x + 30
x + x + x + 30 = 180 → 3x = 150 → x = 50
Angles are: 50°, 50°, and 80°.
Q11. One angle is equal to the sum of the other two. Show that it's a right triangle.
Answer:
Let the three angles be x, y, and z.
Suppose x = y + z
Then total = x + y + z = 180
Since x = y + z → x + x = 180 → 2x = 180 → x = 90
So, one angle is 90°, which means the triangle is right-angled.