Heath ID: I.19

G.28

In any triangle the greater angle is subtended by the greater side.

Let ABC be a triangle having the angle ABC greater than the angle BCA;

I say that the side AC is also greater than the side AB.

For, if not, AC is either equal to AB or less.

Now AC is not equal to AB; for then the angle ABC would also have been equal to the angle ACB; [G.12] but it is not;

therefore AC is not equal to AB.

Neither is AC less than AB, for then the angle ABC would also have been less than the angle ACB; [G.27] but it is not; therefore AC is not less than AB.

And it was proved that it is not equal either. Therefore AC is greater than AB.

Therefore etc.

Q. E. D.

Dependency Graph

Required for

G.30, G.31, G.32, G.34, G.35