how to solve theorum 8.3 of class 9 cbse
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Given - A quadrilateral ABCD .
To Prove - ABCD is a parallelogram
AB || DC and AD ||BC
Construction - Join Aand C
Proof - In ΔABC and ΔDCA
AB = DC ( given )
AD = BC (given)
AC = AC (common)
Therefore, ΔABC ~= ΔCDA [By SSS ]
Δ1 = Δ3 ( cpct )
Δ2 = Δ4 (cpct )
but these are alternate number and whenever alternate angles are equal, the lines are parallel
Therefore, AB || DC and AD || BC
ABCD is a parallelogram
I Hope Help You..
Given - A quadrilateral ABCD .
To Prove - ABCD is a parallelogram
AB || DC and AD ||BC
Construction - Join Aand C
Proof - In ΔABC and ΔDCA
AB = DC ( given )
AD = BC (given)
AC = AC (common)
Therefore, ΔABC ~= ΔCDA [By SSS ]
Δ1 = Δ3 ( cpct )
Δ2 = Δ4 (cpct )
but these are alternate number and whenever alternate angles are equal, the lines are parallel
Therefore, AB || DC and AD || BC
ABCD is a parallelogram
I Hope Help You..
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