Course Content
Class 7th Science
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Class 7th Math
0/71
Class 7 Social Science Geography
0/20
Class 7 Social Science History
0/20
Class 7 Social Science Civics
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Class 7 English Honeycomb
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Class 7 English Honeycomb Poem
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Class 7 English An Alien Hand Supplementary
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Online Class For 7th Standard Students (CBSE)
About Lesson

## Introduction

### Triangle

• A triangle is a closed curve made of three line segments.

• It has three:Sides:
(i) Sides: ¯¯¯¯¯¯¯¯AB, ¯¯¯¯¯¯¯¯BC and ¯¯¯¯¯¯¯¯CA
(ii) Angles: ∠BAC, ∠ACB and ∠CBA
(iii) Vertices: A, B and C

## Important Lines in a Triangle

### Median

• Median is the line that connects a vertex of a triangle to the mid-point of the opposite side.
• In the given figure, ¯¯¯¯¯¯¯¯¯AD is the median, joining the vertex A to the midpoint of ¯¯¯¯¯¯¯¯BC.

### Altitude

• An altitude is a line segment through a vertex of the triangle and perpendicular to a line containing the opposite side.

## Sides Also Have Constraints

### 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.

• In the above triangle,
9+11=20 >14
11+14=25 >9
9+14=23 >11

### Difference between lengths of two sides of a triangle

• The difference between lengths of any two sides is smaller than the length of the third side.

• In the above triangle,
11 – 9 = 2 < 14
14 – 11 = 3 < 9
14 – 9 = 5 < 11
• Using the concept of sum of two sides and difference of two sides, it is possible to determine the range of lengths that the third side can take.

## Triangle Properties

### Angle sum property of a triangle

• The total measure of the three angles of a triangle is 1800.

• In △PQR,
∠RPQ+∠PQR+∠QRP
=70+ 60+ 50= 1800

### Exterior angle of a triangle and its property

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

In the given figure, ∠1+∠2=∠3.

### Pythagoras Theorem

• The side opposite to the right angle in a right-angled triangle is called the hypotenuse.
• The other two sides are known as legs of the right-angled triangle.
• In a right-angled triangle, square of hypotenuse is equal to the sum of squares of legs.

AC2=AB2+BC2
⇒52=42+32

### Properties of isosceles and equilateral triangles

Properties of Isosceles Triangle

• Two sides are equal in length.
• Base angles opposite to the equal sides are equal.

Properties of Equilateral Triangle

• All three sides are equal in length.
• Each angle equals to 600.

## Classification of Triangles

### Classification of triangles based on sides

• Equilateral triangle: A triangle in which all the three sides are of equal lengths.
• Isosceles triangle: A triangle in which two sides are of equal lengths.
• Scalene Triangle: A triangle in which all three sides are of different length.

### Classification of triangles based on angles

• Acute-angled: A triangle with three acute angles.
• Right-angled: A triangle with one right angle.
• Obtuse-angled: A triangle with one obtuse angle.

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