Q8 of 62 Page 180

In the figure DE||AB and DF||AC.

Prove that EF||BC.


Given: DE||AB and DF||AC

Required: To prove EF||BC.


Consider ΔAPB


Here, ED||AB


∴ By Thales theorem --eq(1)


Now, Consider ΔPAC


Here, DF||AC


∴ By Thales theorem --eq(2)


From –eq(1) and –eq(2), we can see that



∴ By Converse Thales theorem we can say that EF||BC in ΔPBC (∵)


Hence Proved


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