In âłABc P&.are the Midpoint ABand Bemid Point AB pier{ that auaar

1.	In âłABc P&.are the Midpoint ABand Bemid Point AB pier{ that auaare ĺąątue
Answer» Let ABC is a triangle. P andQ are the mid points of AB and BC respectivelyand R is the mid-point of AP. Join PQ, QR, AQ, PC, RC as shown in thefigure. Now we know that median of a triangle divides it into two triangle of equal areas. In triangle CAP, Cr is the mid point. So Area(ΔCRA) = (1/2)* Area(ΔCAP) .......1 Again in triangle CAB, CP is the mid point. So Area(ΔCAP) = (1/2)* Area(ΔCPB) ............2 from eqaution 1 and 2, we get Area(ΔCAP) = (1/2)Area(ΔCPB) ..............3 Again in triangle PBC, PQ is the mid point. So (1/2)Area(ΔCPB) = Area(ΔPBQ) ............4 From equation 3 and 4, we get Area(ΔARC) = Area(ΔPBQ) ...............

In âłABc P&.are the Midpoint ABand Bemid Point AB pier{ that auaare ĺąątue

Answer»

Let ABC is a triangle. P andQ are the mid points of AB and BC respectivelyand R is the mid-point of AP.

Join PQ, QR, AQ, PC, RC as shown in thefigure.

Now we know that median of a triangle divides it into two triangle of equal areas.

In triangle CAP, Cr is the mid point.

So Area(ΔCRA) = (1/2)* Area(ΔCAP) .......1

Again in triangle CAB, CP is the mid point.

So Area(ΔCAP) = (1/2)* Area(ΔCPB) ............2

from eqaution 1 and 2, we get

Area(ΔCAP) = (1/2)*Area(ΔCPB) ..............3

Again in triangle PBC, PQ is the mid point.

So (1/2)*Area(ΔCPB) = Area(ΔPBQ) ............4

From equation 3 and 4, we get

Area(ΔARC) = Area(ΔPBQ) ...............