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PYTHAGORAS THEOREM
PYTHAGORAS THEOREM
Pythagoras theorem is used to solve problems involving right angled triangles.
Pythagoras theorem is used to solve problems involving right angled triangles.
Statement:
In a right- angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides.
Shown below
Required to prove: c2 = a2 + b2
Construction : Joining L and N. Considering the trapezium PQLN:
Area of the trapezium
but area of trapezium = area Δ PKN + area Δ KQL + area Δ KLN
(a+b) (a+b) = ab + ( c x c) (a+b) (a+b) = ab + c2 [a2 + 2ab + b2] = ab + c2 a2 + ab + b2 = ab + c2
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a2 + b2 = c2 Pythagoras theorem
Examples
1.The side s of a triangle containing the right angle have length of 5cm and 12cm.
Find the length of the hypotenuse
Solution
C2= a2 +b2
C2 = 52 + 122
C2 = 25+ 144
C2 = 169
C = 
C= 13cm
∴ The length of the hypotenuse = 13cm.
2. In figure below if AC =17cm, BC = 8cm, and CD = 12cm find AD
Solution:
EXERCISE
1. Calculate the unknown side of the following triangle
SOLUTION:
172 = 152 + b2
172 = 152 + b2
b2 = 172 – 152
b2 = 289 – 225
b = 
b = 8cm
∴ r2 = 82+ 82
r2 = 64 +64
r2 = 64 +64
∴ r =11.31cm
2. Given triangle ABC, where B = 900.Find the lengths of the sides which are not given
3. A man travels 15km due north and then 8km due west. How far is he from his starting point?
Solution:
X2 = 152 +82
X2 = 225 +64
X = 
X = 17km
∴ He is 17km from his starting point
Find the area of the triangle and the length of the perpendicular from C to B.
Solution:
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