If the diagonals of a parallogram …

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If the diagonals of a parallogram are 12cm and 16cm find the length of each segment of the diagonals into which they are divided. State the property of parallelogram used.

Posted by Harsh Gupta 6 years, 6 months ago

CBSE > Class 08 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

12 cm is divided into 6 cm each, 16 cm is divided into 8 cm each

Step-by-step explanation: In the parallelogram, opposite sides are equal & parallel

Let say ABCD is a parallelogram & Diagonals AC & BD intersect at O
Now comparing Δ AOB & ΔCOD
∠AOB = ∠COD ( opposite angles)
∠ABO = ∠CDO ( ad BD is cutting two ║ lines AB & CD)
Similarly ∠BAO = ∠DCO ( ad AC is cutting two ║ lines AB & CD)
So Δ AOB ≅ ΔCOD
AO/CO = BO/DO = AB/CD
AB = CD
=> AO/CO = BO/DO = 1
=> AO = CO & BO = DO
AO + CO = AC => AO = CO = AC/2
BO + DO = BD => BO = DO = BD/2

Hence Diagonals are bisected
Diagonal 12 cm is divided into 6 cm each
Diagonal 16 cm is divided into 8 cm each

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