# NCERT Class 7 Maths Chapter 6 The Triangle and Its Properties Notes and Solutions PDF

In NCERT Class 7 Maths Chapter 6, The Triangle and Its Properties, we will study the concept of different triangles, their properties, and how to determine certain aspects of a triangle such as its median, altitude (or height of a triangle) and the exterior & interior angles of a triangle. Students will also learn the angle sum property of a triangle. In the later part of this chapter, students will learn about the elation and differences between an equilateral and an isosceles triangle in detail. Let us now have a look at the NCERT Class 7 Maths Chapter 6 The Triangle and Its Properties Notes and Solutions (PDF).

## NCERT Class 7 Maths Chapter 6 Notes – PDF Available

Check the topic-wise notes for NCERT Maths Class 7 – Chapter 6 below. You can also download the PDF of the notes and take a printout to study later when you need quick revision before going to the e𝑥am hall.

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### Topic 1: Medians of a Triangle

A median connects a vertex of a triangle to the mid-point of the opposite side.

In the above diagram, AD is the median of the triangle ABC.

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### Topic 2: Altitudes of a Triangle

The height is given by the line segment that starts from the vertex of the triangle, comes straight down to the opposite side and is perpendicular to it.

### Topic 3: Exterior Angle of a Triangle and its Property

In the figure given below, ∠ACD is the exterior angle.

Property of the exterior angle of a triangle: An exterior angle of a triangle is equal to the sum of its interior opposite angles.

### Topic 4: Angle Sum Property of a Triangle

This property establishes the relation between all the three angles of a triangle. The angle sum property of a triangle states that – the sum of the measures of the three angles of a triangle is 180°.

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### Topic 5: Case of Special Triangles

1. Equilateral Triangle: A triangle in which all three sides are of equal lengths is called an equilateral triangle. In this triangle, each angle measures 60°.
2. Isosceles Triangle: A triangle in which two sides are of equal lengths is called an isosceles triangle. In this triangle, the base angles opposite to the equal sides are equal.

### Topic 6: Sum of the Lengths of Two Sides of a Triangle

The sum of the lengths of any two sides of a triangle is greater than the third side.

### Topic 7: Right-Angled Triangles and Pythagoras Property

1. Hypotenuse: In a right-angled triangle, the side opposite to the right angle is called the hypotenuse; the other two sides are known as the legs of the right-angled triangle.
2. Pythagoras Property: In a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the legs. For any right-angled triangle, the Pythagoras property holds.

This property can also give a very useful result – if the Pythagoras property holds, the triangle must be right-angled.

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## Chapter 6, The Triangle and Its Properties Solutions – PDF Available!

Below we have provided solutions for NCERT Class 7 Maths Chapter 6, The Triangle and Its Properties. Go through for answers to some important questions.

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### E𝑥ercise 6.1 Solutions

Q 1. In Δ PQR, D is the mid-point of.

is _________________.

PD is _________________.

Is QM = MR?

Solutions. The answers are given below.

1. PM is the altitude of the triangle as it starts from the vertex of the triangle, comes straight down to the opposite side, and is perpendicular to it.
2. PD is the median of the triangle as one end is connected to the vertex P and another to the mid-point of the opposite side.
3. Since the median of the triangle, ΔPQR cuts QR at point D, so, D is the mid-point of the line segment.

∴ QM ≠ MR.

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### Exercise 6.2 Solutions

Q 1. Find the value of the unknown exterior angle 𝑥 in the following diagrams:

Solutions. The answers are given below.

1. We know that the exterior angle of a triangle is equal to the sum of its interior opposite angles.

∴ 𝑥 = 65° + 45° ⇒ 𝑥 = 130°

1. Similar to (a), 𝑥 = 50° + 50° ⇒ 𝑥 = 100°

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Q 3. Find the value of the unknown interior angle 𝑥 in the following figures:

Solutions. We know that the exterior angle of a triangle is equal to the sum of its interior opposite angles. Now, the solutions to the given questions are given below.

1. From the property stated above, we get:

𝑥 + 50° = 115° ⇒ 𝑥 = 115° – 50° = 65°

∴ 𝑥 = 65°

1. From the property stated above, we get:

𝑥 + 30° = 80° ⇒ 𝑥 = 80° – 30° = 50°

∴ 𝑥 = 50°

1. From the property stated above, we get:

𝑥 + 60° = 120° ⇒ 𝑥 = 120° – 60° = 60°

∴ 𝑥 = 60°

1. One of the interior angles (opposite to the exterior angle of the given triangle) measures 90° (right-angled). So, from the property stated above, we get:

𝑥 + 90° = 125° ⇒ 𝑥 = 125° – 90° = 35°

∴ 𝑥 = 35°

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### E𝑥ercise 6.3 Solutions

Q 1. Find the value of the unknown 𝑥 in the following diagrams:

Solutions. The answers are given below.

1. We know that the sum of all three interior angles of a triangle is 180°. So, from the given figure, we get:

𝑥 + 50° + 60° = 180°

∴ 𝑥 =  180° – 50° – 60°

⇒ 𝑥 =  180° – 110° = 70°

Hence, 𝑥 =  70°

1. The given triangle is right-angled. So, from the given figure, we get:

𝑥 + 2𝑥 + 90° = 180°

∴ 3𝑥 =  180° – 90°

⇒ 3𝑥 =  90°

⇒ 𝑥 = 90°/3 = 30°

So, 𝑥 =  30° and 2𝑥 =  30° × 2 = 60°

Hence, the three angles in the given triangle measure 30°, 60° and 90°.

## FAQs

Q.1. What are complementary angles?

Ans: When the sum of the measures of two angles is 90°, the angles are called complementary angles.

Q.2. What are supplementary angles?

Ans: When the sum of the measures of two angles is 180°, the angles are called complementary angles.

Q.3. What is a transversal?

Ans: A line that intersects two or more lines at distinct points is called a transversal.

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This was all about NCERT Class 7 Maths Chapter 6, The Triangle and Its Properties in which we studied different angles and their properties. We also studied the properties of angles in relation to each other. Download the NCERT Class 7 Maths Chapter 6 Notes and Solutions PDF to ace your e𝑥am preparations. Follow the CBSE Class 7 Maths Solutions and Notes for more such chapter notes and important questions and answers for preparation for CBSE Class 7 Maths.