Abcd Quadrilateral Fig Line Through Parallel Meets Produced In Prove Ar В–Іabp Ar Quad Abcd

ABCD is a quadrilateral [Fig. 9.26]. A line through D, parallel to AC meets BC produced in P. Prove ar (△ABP) = ar (quad. ABCD).


Solution   :-

Given: A quadrilateral ABCD in which DPII AC 

To prove:  ar (ABP) = ar (quad. ABCD) 

Proof:   △ACP and ACD are on same base AC and between same parallels AC and DP.

 ⇒ ar (ACP) = ar (ACD) 

Adding, ar (ABC) on both sides,

 ar ( ABC) + ar (△ACP) = ar (ABC) + ar (ACD) 

                               ar (ABP) = ar (quad. ABCD)