1. Additional Example 3 Additional Example 4
6.2 Pythagoras’ Theorem
Additional Example 3
Additional Example 4
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2. Additional Example 3
In the figure, BAC = ACD = 90, AB = 9, BC = 15 and CD = 16. Find
(a) AC,
Solution
(b) AD.
Solution
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3. Solution In ABC, (a) BC2 = AB2 + AC2 (Pyth. Theorem) 152 = 92 + AC2
Additional Example 3
In the figure, BAC = ACD = 90, AB = 9, BC = 15 and CD = 16. Find
Solution
(a) AC,
(b) AD.
(a)
In ABC,
BC2 = AB2 + AC2 (Pyth. Theorem)
152 = 92 + AC2
AC2 = 144
AC cannot be negative because it is the length of a side.
 AC = 12
Q3(b)
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4. Solution In ACD, (b) AD2 = AC2 + CD2 (Pyth. Theorem) = 122 + 162
Additional Example 3
In the figure, BAC = ACD = 90, AB = 9, BC = 15 and CD = 16. Find
Solution
(a) AC,
(b) AD.
(b)
In ACD,
AD2 = AC2 + CD2 (Pyth. Theorem) =
= 400
AD cannot be negative because it is the length of a side.
 AD = 20
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5. Additional Example 4
The figure shows an isosceles trapezium ABCD. Find its area.
Solution
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6. Solution  ABCD is an isosceles trapezium.  AE = (AD – BC)
Additional Example 4
The figure shows an isosceles trapezium ABCD. Find its area.
Solution
 ABCD is an isosceles trapezium.
 AE = (AD – BC)
= (28 – 10)
= 9
AB2 = BE2 + AE2 (Pyth. Theorem)
152 = BE2 + 92
BE2 = 144
 BE = 12
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7. Solution Area of trapezium ABCD = (BC + AD)  BE
Additional Example 4
The figure shows an isosceles trapezium ABCD. Find its area.
Solution
Area of trapezium ABCD
= (BC + AD)  BE
= ( )  12 square units
= 228 square units
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