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 PR 2 = PQ 2 + QR 2 Or c 2 = a 2 + b 2 P QR a b c

c = a = b = a b c FINDING THE LENGTH OF THE MISSING SIDE OF A RIGHT-ANGLED TRIANGLE

EXAMPLE 1: In the figure below, ABC is a right-angled triangle. Find the lenght of AC. A B 4 cm C 3 cm Solution: AC= = = = = 5 cm

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 15 m 17 m x Using Pythagoras’ Teorem X = = AREA = 15m X 8m = 120 m 2

LETS TRY A FEW EXERCISES…… LETS TRY A FEW EXERCISES……