STD 8 MATHEMATICS LESSON.

PYTHAGOREAN RELATIONS.

The Pythagoras theorem.
This only applies to right-angled triangles.
The longest side is called hypotenuse and is usually opposite the right angle.
The shorter side is called opposite or height and the other side is adjacent or base.
If we say hypotenuse side is C and height is A and base is B, then the theory states that : a² + b² = c²

look at these figures.



 i) Are you able to identify hypotenuse, base and height?
ii) Can you be able to calculate one side given the other two?

Example

Find x?
Working
If the measure of hypotenuse is c and the other a and b, 
then: √a² + √b² = √c². 
We can say that : a² + b² = c²
∴ 3² + 4² = x²
∴ 9 + 16 = X²
∴ 25 = X²
∴ X = √25
X=5

Exercise.


1. Calculate the height of the wall up to where the ladder is.

Deselect Answer

2. Calculate line BC. Deselect Answer

3. Line AB is the hypotenuse of triangle ABC. If line AB is 13 cm and line AC is 12 cm, what is the length of line BC?Deselect Answer

4. A right-angled triangle XYZ has has a base of  8 cm and a height of 15 cm. What is its hypotenuse?Deselect Answer

5. If a = 6 cm and b is 8 cm, what is c?Deselect Answer

6. A right angled plot has sides 20 cm and 25 cm as the longest side. What is the length of the other side?Deselect Answer

7. A right-angled triangle has an area of 30 cm². If the base is 12 cm, what is its hypotenuse?Deselect Answer

8. Which one of the following is not a part of pythagoras theorem?Deselect Answer