pythagoras’ theorem what is a right-angled triangle ? a right-angled triangle is a triangle with...
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PYTHAGORAS’ THEOREM
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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
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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
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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
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• 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
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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
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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
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Solution:• Let the width = x cm
225289
15 m
17 mx
Using Pythagoras’ Teorem
X =
=
=
=
22 1517
64m8
AREA = 15m X 8m
= 120 m2
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LETS TRY A FEW EXERCISES……
LETS TRY A FEW EXERCISES……