PYTHAGORAS’ THEOREM

WHAT IS A RIGHT-ANGLED TRIANGLE ?

A RIGHT-ANGLED TRIANGLE IS A TRIANGLE

WITH ONE OF THE ANGLES IS A RIGHT

ANGLE

A

B C

THE HYPOTENUSE OF A RIGHT- ANGLED TRIANGLE IS THE LONGEST SIDE WHICH IS OPPOSITE THE RIGHT ANGLE.

A

B C

HYPOTENUSE

AC is the hypotenuse because AC is the longest side

WHAT IS A

HYPOTENUSE

PYTHAGORAS’ THEOREM STATES RELATIONSHIP BETWEEN THE LENGTHS OF

THE SIDES OF A RIGHT-ANGLED TRIANGLES

PHYTAGORAS’ THEOREM

Pythagoras’ theorem states that if PQR is a right-angled triangle, then

PR2 = PQ2 + QR2

Or

c2 = a2 + b2

P

Q R

a

b

c

• c2 = a2 + b2

• c =

• a =

• b =

a

b

c

FINDING THE LENGTH OF THE MISSING SIDE OF A RIGHT-ANGLED

TRIANGLE

22 ba

22 bc 22 ac

EXAMPLE 1:

In the figure below, ABC is a right-angled triangle. Find the lenght of AC.

A

B

4 cm

C3 cm

Solution:

AC =

=

=

=

= 5 cm

22 BCAB 22 34

916

25

EXAMPLE 2 :

A rectangular billboard is 15 m long. The length of its diagonal is 17 m. Find the area of the billboard.

15 m

17 m

Solution:• Let the width = x cm

225289

15 m

17 mx

Using Pythagoras’ Teorem

X =

=

=

=

22 1517

64m8

AREA = 15m X 8m

= 120 m2

LETS TRY A FEW EXERCISES……

LETS TRY A FEW EXERCISES……