Question

In the figure QP IS PARALLEL to XY,QX is parallel to PR and PY is parallel to QR. Prove that ar(triangle QXR)= ar(triangle PYR)

Answer 1

Answer:

Step-by-step explanation:

pq||xt(xt is a part of xy)

similarly,qx||pt(pt is a part of pr)

therefore

pqxt is a||gm

similarly pq||sy

qs||py

therefore

pqsy is a ||gm

now,,IIgm pqsy and IIgm pqxt lie on the same base xy and between same || lines pq and xy

therefore, ar.(pqsy)=ar(pqxt).......(1)

now, triangle qxr and ||gm pqxt lie on the same base qx and between same|| lines qx and pr

therefore, ar.(qxr)=1/2ar(pqxt).....(2)

similarly, triangle pyr and||gm pqsy lie on the same base py and between same || lines py and qr

​therefore, ar.(pyr)=1/2ar.(pqsy).....(3)

    from(1),(2)and(3)

ar.(qxr)=ar.(pyr)

     h.p.