Marks' first lessons in geometry / In two parts. Objectively presented, and designed for the use of primary classes in grammar schools, academies, etc.

by Bernhard Marks

Then, if the angles a and b, on the one hand, and the angle b c d, on the other, are separately equal to the angles b c e, e c d,

What have you found out?

What axiom have you just employed?

To what same thing have you found two other things equal?

What two things did you find equal to it?

DEMONSTRATION.

We wish to prove, that,

If any side of a triangle be produced, the new angle formed will be equal to the sum of the angles that are not adjacent to it.

Let a b c be a triangle.

Produce the side a c to d; then will the new angle b c d be equal to the sum of the angles a and b.