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Question

ABCD is a rhombus with diagonals AC and BD.
The value of p+q+r+s+t is . (3 marks)

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Solution

In the rhombus ABCD,
A+B+C+D=360 [Angle sum property]

In AED and AEB,AB=AD [Sides of rhombus]AE=AE [Common side]AED=AEB[Diagonals of a rhombus bisect at 90]AEDAEB

DAC=CAB=12DAB
[CPCT]
p=12A
A=2p (1.5 marks)

Similarly,
B=2q, C=2t and D=2s
2p+2q+2t+2s=360
p+q+t+s=180

The diagonals of a rhombus intersect at 90
AEB=r=90

Therefore, p+q+r+s+t=180+90
p+q+r+s+t=270 (1.5 marks)


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