Geometry and Mensuration: Test 14

Since the points P and Q are the centroids, therefore PQ = 1/3 of BD.
Thus PQ = 1/3 of 18 cm = 6 cm.

We know that: Triangles ΔAPC and ΔBCP have the common base PC.
Also, the two triangles ΔAPC and ΔBCP are located between the same two parallel lines: AB and PC
Thus, we can say: AD||CQ and AD=CQ……………………….i
From the above, we can conclude ADQC is a parallelogram.
Also, triangles ΔADC and ΔDAQ have the common base: AD
Also, the two triangles ΔADC and ΔDAQ are located between the same two parallel lines: AD and CQ.
Thus, we can conclude: Area of Δ( ADC)= Area of Δ( ADQ)
Let’s subtract area of ( DADP) from both sides: area of Δ( APC)= area of Δ( DPQ)……..(ii)
From (i) and (ii), we can conclude: area of Δ( BPC) = area of Δ( DPQ)

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