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Triangle PQR is an equilateral triangle with PM perpendicular to QR.Show that area of triangle PQM = area if triangle PRM.



Given :
PQR is an eq triangle
TP : ar(Δ PQM) = ar(Δ PRM)

Proof : PQ = PR= QR ⇒ 1
 angle PMR = angle PMQ = 90 degree (PM ⊥QR )
in Δ PMQ and Δ PMR,
PQ = PR ( From 1)
PM=MP (Common side)
Δ PMQ is congruent to Δ PMR (by SAS rule )
since they are congruent , they will have the same area
∴ ar(Δ PMQ) = ar(ΔPMR)
     hence proved

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