Abcde Pentagon Drawn Parallel Meets Produced Drawn Parallel Meets Produced Prove Abcde

In Fig. 9.30, ABCDE is any pentagon. BP drawn parallel to AC meets DC produced at P and EQ drawn parallel … at Q. Prove that ar…

Answers:

Solution   :-

Since, △ABC and △APC are on the same base AC and between the same parallels BP and AC

 ∴  ar (△ABC) = ar (△APC)…..(i) 

(Triangles on the same base and between the same parallels are equal in area) 

Similarly, EQ II AD 

 ∴  ar (△AED) = ar (AQD) …(ii)

 Adding (i) and (ii), and then adding ar (△ACD) to both the sides, we get 

ar (△ABC) + ar (△AED) + ar (ACD) = ar (△APC)+ ar (△AQD) + ar (△ACD) 

⇒     ar(ABCDE) = ar(APQ).