For let AD be produced in both directions to G, H; through B let BG be drawn parallel to CA, [[I. 31](elem.1.31)] and through F let FH be drawn parallel to DE.

Then each of the figures GBCA, DEFH is a parallelogram; and GBCA is equal to DEFH;

for they are on equal bases BC, EF and in the same parallels BF, GH. [[I. 36](elem.1.36)]

Moreover the triangle ABC is half of the parallelogram GBCA; for the diameter AB bisects it. [[I. 34](elem.1.34)]

And the triangle FED is half of the parallelogram DEFH; for the diameter DF bisects it. [[I. 34](elem.1.34)]

[But the halves of equal things are equal to one another.]

Therefore the triangle ABC is equal to the triangle DEF.

Therefore etc.

Q. E. D.