Draw Triangles with Given Condition

Key Concepts

1. Understanding the triangle and its parts
2. Types of triangles
3. Triangle and its properties
4. The sum of all internal angles of a triangle is always equal to 180°
5. The sum of the length of any two sides of a triangle is greater than the length
   of the third side
6. 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 

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

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

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

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

5. 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. 

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

7. Area of a triangle = ½ × Base × Height 

8. 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:

1. 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