### Key Concepts

- Understanding the triangle and its parts
- Types of triangles
- Triangle and its properties
- The sum of all internal angles of a triangle is always equal to 180°
- The sum of the length of any two sides of a triangle is greater than the length

of the third side - Understand Equilateral, Isosceles, Scalene triangles

**Different Types of Triangles**

**The types of triangles are classified based on: **

**The lengths of their sides**

**Interior angles**

**9.3.1 Draw triangles with given conditions**

Classification of triangles according to the length of their sides

We can classify triangles into 3 types based on the lengths of their sides:

Scalene

Isosceles

Equilateral

### Isosceles Triangle

An isosceles triangle is a triangle in which two sides and two angles are equal. Equal lengths of a triangle are shown by making an arc on each side.

In the diagram above, the length of side *AB* = *AC* and ∠ *ABC* =∠ *ACB*.

**Equilateral triangle:** An equilateral triangle has all three sides equal, and all three interior angles equal, too. In this case, each interior angle of an equilateral triangle is 60 degrees

### Scalene Triangle

A scalene triangle is a triangle in which all the sides have different measures and all the interior angles are also different.

### Properties of Triangle

- The sum of all the angles of a triangle (of all types) is equal to 180°.

- The sum of the length of the two sides of a triangle is greater than the length of the third side.

- In the same way, the difference between the two sides of a triangle is less than the length of the third side.

- The side opposite the greater angle is the longest side of all the three sides of a triangle.

- The exterior angle of a triangle is always equal to the sum of the interior opposite angles. This property of a triangle is called an exterior angle property.

- Two triangles are said to be similar if their corresponding angles of both triangles are congruent and the lengths of their sides are proportional.

- Area of a triangle = ½ × Base × Height

- The perimeter of a triangle = sum of all its three sides

**TOPIC: Draw triangles with given side lengths**

**9.3.2 Determine possible side lengths of triangle**

Use the following picture of rational numbers to answer the following questions:

**Example 1:**

Check whether it is possible to have a triangle with the given side lengths.

7,9,13

Add any two sides and see if it is greater than the other side.

The sum of 7 and 9 is 16 and 16 is greater than 13.

The sum of 9 and 13 is 21 and 21 is greater than 7.

The sum of 7 and 13 is 20 and 20 is greater than 9.

This set of side lengths satisfies the Triangle Inequality Theorem.

## Exercise:

- In ∆ABC, write the following:

- Angle opposite to side BC.
- The side opposite to ∠ABC.
- Vertex opposite to side AC.

2. Classify the following triangle on the bases of sides

3. Fill in the blanks with the correct word/symbol to make it a true statement:

- A triangle has ……. sides.
- A triangle has ……..vertices.
- A triangle has ……..angles.
- A triangle has ………parts.

4. Take three non – collinear points L, M, N. Join LM, MN and NL. What figure do you get?

Name:

(a) The side opposite to ∠L. …………………………….

(b) The angle opposite to side LN. …………………………….

(c) The vertex opposite to side MN. …………………………….

(d) The side opposite to angle N. …………………………….

5. Find the number of triangles in the figure given below:

6. Classify the triangle according to sides, that is, equilateral, isosceles and scalene triangles

(a) 6 cm, 3 cm, 5 cm.

(b) 6 cm, 6 cm, 6 cm.

(c) 7 cm, 7 cm, 5 cm.

(d) 8 cm, 12 cm, 10 cm.

7. Draw any triangle and name it PQR. Measure its sides and classify the triangle as Isosceles triangle, scalene triangle or equilateral triangle.

8. The perimeter of a triangle is 24 cm. Two of its sides are 8 cm and 9 cm. Find the length of its third side.

9. What is a triangle?

10. Find the missing side in the diagram below:

### What have we learnt:

- Understand Triangle and its parts
- Types of triangles
- Triangle and its properties
- The sum of all internal angles of a triangle is always equal to 180°
- The sum of the length of any two sides of a triangle is greater than the length of the third side
- Understand Equilateral, Isosceles and Scalene triangles.

### Concept Map

#### Related topics

#### Addition and Multiplication Using Counters & Bar-Diagrams

Introduction: We can find the solution to the word problem by solving it. Here, in this topic, we can use 3 methods to find the solution. 1. Add using counters 2. Use factors to get the product 3. Write equations to find the unknown. Addition Equation: 8+8+8 =? Multiplication equation: 3×8=? Example 1: Andrew has […]

Read More >>#### Dilation: Definitions, Characteristics, and Similarities

Understanding Dilation A dilation is a transformation that produces an image that is of the same shape and different sizes. Dilation that creates a larger image is called enlargement. Describing Dilation Dilation of Scale Factor 2 The following figure undergoes a dilation with a scale factor of 2 giving an image A’ (2, 4), B’ […]

Read More >>#### How to Write and Interpret Numerical Expressions?

Write numerical expressions What is the Meaning of Numerical Expression? A numerical expression is a combination of numbers and integers using basic operations such as addition, subtraction, multiplication, or division. The word PEMDAS stands for: P → Parentheses E → Exponents M → Multiplication D → Division A → Addition S → Subtraction Some examples […]

Read More >>#### System of Linear Inequalities and Equations

Introduction: Systems of Linear Inequalities: A system of linear inequalities is a set of two or more linear inequalities in the same variables. The following example illustrates this, y < x + 2…………..Inequality 1 y ≥ 2x − 1…………Inequality 2 Solution of a System of Linear Inequalities: A solution of a system of linear inequalities […]

Read More >>
Comments: