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in Quadrilaterals by (27.3k points)
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P is the mid point of side BC of a parallelogram ABCD such that ∠BAP =∠DAP. If AD = 10 cm, then CD = 

A. 5 cm 

B. 6 cm 

C. 8 cm 

D. 10 cm

1 Answer

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by (26.9k points)
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Best answer

Option : (A)

Given, 

ABCD is a parallelogram,

P is mid point of side BC 

∠BAP = ∠DAP 

AD = 10cm 

∵ AD || BC 

∠DAP = ∠APB 

[alternate angles] 

∠DAP = ∠BAP 

AB = BP 

(side opposite to equal angles)

= BP = \(\frac{1}{2}\)BC

∴ AB =  \(\frac{1}{2}\)BC 

\(\frac{1}{2}\) x 10 

= 5 cm

AB = CD = 5cm 

(sides of parallelogram)

Hence, 

CD = 5 cm

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