MNOP is a parallelogram and PN is one of its diagonals. Show that ar(triangle PMN)=ar(trianglePON)
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See the figure,
In ΔPMN and ΔPON
MN = PO (opposite sides are equal)
MP = ON (opposite sides are equal)
And,
NP = NP (common side)
Hence,
ΔPMN ≈ ΔPON (SSS rule)
ar(ΔPMN) = ar(ΔPON) (Congruent Δ's have equal areas)
In ΔPMN and ΔPON
MN = PO (opposite sides are equal)
MP = ON (opposite sides are equal)
And,
NP = NP (common side)
Hence,
ΔPMN ≈ ΔPON (SSS rule)
ar(ΔPMN) = ar(ΔPON) (Congruent Δ's have equal areas)
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