PYTHAGORAS THEOREM Carmelo Ellul AB2 = AC2 + CB2

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Presentation transcript:

PYTHAGORAS THEOREM Carmelo Ellul AB2 = AC2 + CB2 In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other 2 sides. A B C A powerpoint presentation by Carmelo Ellul Head of Department (Mathematics) HYPOTENUSE 1st side 2nd side AB2 = AC2 + CB2

PYTHAGORAS THEOREM AB2 = AC2 + CB2 52 = 32 + 42 25 = 9 + 16 5 cm 3 cm

Finding the length of the hypotenuse PYTHAGORAS THEOREM Problem 1: Finding the length of the hypotenuse

PYTHAGORAS THEOREM By Pythagoras: AB2 = AC2 + CB2 AB2 = 52 + 122 5 cm 12 cm Problem 1: In triangle ABC find the length of side AB. By Pythagoras: AB2 = AC2 + CB2 AB2 = 52 + 122 AB2 = 25 + 144 AB2 = 169 AB = AB = 13 cm

PYTHAGORAS THEOREM By Pythagoras: AB2 = AC2 + CB2 AB2 = 52 + 122 5 cm 12 cm Problem 1: In triangle ABC find the length of side AB. By Pythagoras: AB2 = AC2 + CB2 AB2 = 52 + 122 AB2 = 25 + 144 PROBLEM 2 AB2 = 169 RESTART AB = END SHOW AB = 13 cm

Finding the length of one of the smaller sides PYTHAGORAS THEOREM Problem 2: Finding the length of one of the smaller sides

PYTHAGORAS THEOREM By Pythagoras: PQ2 = PR2 + RQ2 102 = 52 + RQ2 5 cm 10 cm Problem 2: In triangle PQR find the length of side RQ correct to 1 d.p. By Pythagoras: PQ2 = PR2 + RQ2 102 = 52 + RQ2 100 = 25 + RQ2 100 - 25 = RQ2 75 = RQ2 = RQ RQ = 8.660... cm = 8.7 cm

PYTHAGORAS THEOREM By Pythagoras: PQ2 = PR2 + RQ2 102 = 52 + RQ2 5 cm 10 cm Problem 2: In triangle PQR find the length of side RQ correct to 1 d.p. By Pythagoras: PQ2 = PR2 + RQ2 102 = 52 + RQ2 100 = 25 + RQ2 100 - 25 = RQ2 PROBLEM 1 75 = RQ2 RESTART = RQ END SHOW RQ = 8.660... cm = 8.7 cm