ABCD is a trapezium with AB||CD and ANGLE BCD=2 ANGLE DAB. if DC=a and BC=b, the length of AB in terms of a and b is____ A) 2a+2b B) 2a+b C) a+2b D) a+b
Answers
Given : ABCD is a trapezium with AB||CD and ∠BCD = 2∠DAB
DC = a & BC = b
To Find : length of AB in terms of a and b
Solution:
ABCD is a trapezium
AB || CD
Draw a line CP || AD
APCD will be a parallelogram
AP = DC = a .....Eq1
opposite angle of parallelogram are equal
Hence ∠PCD = ∠DAB ( ∠DAB = ∠DAP as P lies on AB )
∠BCD = 2∠DAB
∠BCD = ∠PCD + ∠PCB
=> ∠PCD + ∠PCB = 2∠DAB
=> ∠DAB + ∠PCB = 2∠DAB
=> ∠PCB = ∠DAB
∠DAB = ∠CPB ( corresponding angles as CP || AD , & AB is traversal )
=> ∠PCB = ∠CPB
in Δ CPB
∠PCB = ∠CPB
=> PB = BC = b ....Eq2
AB = AP + PB
From Eq1 & Eq 2
=> AB = a + b
option D is correct
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