if ABCD is a parallelogram the prove that
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AB=AB(common)
AD=BC(opposite sides of ||gm are equal)
Angle A=Angle C(90°)
Thus triangle ABD=~ triangle BCD(S. A. S. axiom)
AD=BC(opposite sides of ||gm are equal)
Angle A=Angle C(90°)
Thus triangle ABD=~ triangle BCD(S. A. S. axiom)
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Answer:
Step-by-step explanation:
Given:
A parallelogram ABCD circumscribing a circle.
To Prove:
ABCD is a rhombus?
Solution: See the figure above , we have
AB = DC {Opposite sires of ||gm}
AD = BC {Opposite sires of ||gm}
As we know that length of two tangents drawn from a external points to a circle are equal to each other.
Let's see the tangents form each point
AP = AS {from point A}.....i
BP = BQ {from B}.....ii
CR = CQ {from C}.....iii
DR = DS {from D}.....iv
Now,
➯ AP + BP + CR + DR = BQ + CQ + AS + DS
➯ AB + CD = BC + AD
➯ 2AB = 2AD (opposite sides are equal)
➯ AB = AD
∴ABCD is a ||gm with adjacent sides AB = AD. Hence, is a rhombus.
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