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A gardener has to put a double fence all around a triangular path with sides 120m, 80m and 60m.
In the middle of each side there is a gate of width 10m.
The perimeter of triangle = Sum of all sides
= 120+80+60 = 260 m
Now , the length of wire needed for fence = 2 x ( Perimeter of triangle - 3(10))
= 2 x(260-30) = 2 x (230) = 460 m
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Gaurav Seth 3 years, 11 months ago
Given: A quadrilateral ABCD in which AB ║ DC and AB = DC.
To Prove: ABCD is a parallelogram
i.e., AB ║ DC and AD ║ BC.
Construction: Join A and C.
Proof : Since AB is parallel to DC and AC is transversal
∠BAC = ∠DCA [Alternate angles]
AB = DC [Given]
And AC = AC [Common side]
⇒ ∆BAC ≅ ∆DCA [By SAS]
⇒ ∠BCA = ∠DAC [By cpctc]
But these are alternate angles and whenever alternate angles are equal, the lines are parallel.
⇒ AD ║ BC
Now, AB ║ DC (given) and AD ║ BC [Proved above]
⇒ ABCD is a parallelogram
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