6th Standard Maths Term 2 Unit 4 Geometry - Types and Properties of Triangles

Chapter: 6th Maths : Term 2 Unit 4 : Geometry

Types and Properties of Triangles

Types and Properties of Triangles

Some triangles are drawn in the dotted sheet. Try to draw as many triangles as you can. Then, measure the sides and angles of all triangles and fill the table given below

In a triangle, we observe the following:

• If the measure of all angles are different, then all sides are different.
• If the measure of two angles are equal, then two sides are equal.
• If the measure of three angles are equal, then three sides are equal and each angle measures 60°.

Sum of three angles of a triangle is 180°.

Activity: Forming Triangles with Sticks

Students are divided into groups and each group is given 3 sticks of length 9 units, 2 sticks of length 3 units, 2 sticks of length 2 units, 1 stick of length 5 units and 1 stick of length 4 units. Using the given sticks they are asked to form three triangles, find the length of the sides of each triangle and tabulate them.

1. Was each group able to form 3 triangles?
2. In each of the triangle formed, how many sides are equal?

1. Types of triangle based on its sides

i) If three sides of a triangle are different in lengths, then it is called a Scalene Triangle

Examples:

ii) If any two sides of a triangle are equal in length, then it is called an Isosceles Triangle

Examples:

iii) If three sides of a triangle are equal in length, then it is called an Equilateral Triangle

Examples:

Try these: Complete the following table. In any triangle,

2. Types of triangle based on its angles

Write the given angles as acute, obtuse or right angle formed by two line segments AB and AC

∠A is acute angle | ∠B is acute angle | ∠C is acute angle

∠A is right angle | ∠B is acute angle | ∠C is acute angle

∠A is obtuse angle | ∠B is acute angle | ∠C is acute angle

(i) If three angles of a triangle are acute angles (between 0° and 90°), then it is called an Acute Angled Triangle.

(ii) If an angle of a triangle is a right angle (90°), then it is called a Right Angled Triangle.

(iii) If an angle of a triangle is an obtuse angle (between 90° and 180°), then it is called an Obtuse Angled Triangle.

Try these: Complete the table

DO YOU KNOW: A triangle can have three acute angles, but cannot have more than one right angle or an obtuse angle.

Activity: Name Triangles in Two Ways

In the given figure, there are some triangles. Measure their sides and angles and name them in two ways. (One is done for you )

3. Triangle Inequality property

Think about the situation:

Three students Kamala, Madhan and Sumathi are asked to form triangles with the given sticks of measure 6cm, 8cm, 5cm; 4cm, 10cm, 5cm and 10cm, 6cm, 4cm respectively. While Kamala is successful, Madhan and Sumathi struggle. Why?

To form a triangle the sum of two smaller sides must be greater than the third side. Thus,

In a triangle, the sum of any two sides of a triangle is greater than the third side. This is known as Triangle Inequality property.

AB + BC > CA | BC + CA > AB | CA + AB > BC

Note: If three sides are equal in length, then definitely a triangle can be formed.

DO YOU KNOW: If two sides of the triangle are given, then the length of the third side will lie between the difference and sum of the lengths of two given sides.

Example 1: Can a triangle be formed with 7cm, 10cm and 5cm as its sides?
Solution: Sum of two smaller sides = 5 + 7 = 12cm > 10cm. Yes, a triangle can be formed.

Example 2: Can a triangle be formed with 7cm, 7cm and 7cm?
Solution: Yes, if three sides are equal, triangle inequality is satisfied.

Example 3: Can a triangle be formed with 8cm, 3cm and 4cm?
Solution: Sum of two smaller sides = 3 + 4 = 7cm < 8cm. No, a triangle cannot be formed.

Try these: Can a triangle be formed with the given sides?

Example 4: Can a triangle be formed with angles 80°, 30°, 40°?
Solution: Sum = 80 + 30 + 40 = 150° (≠ 180°). No, a triangle cannot be formed.

Think: Can the difference between two larger sides be less than the third side?

Triangle Game: Connect dots to close triangles and win points!

ANSWERS: Exercise 3.2 Summary

1. Gain = ₹15 | 2. Loss = ₹50 | 3. Profit = ₹200 | 4. Profit = ₹1,00,000
5. Gain = ₹32 | 6. M.P. = ₹29 | 7. Profit = ₹960 | 8. Profit = ₹3000