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

DEMONSTRATION.

We wish to prove that

The three angles of any triangle are equal to two right angles.

Let the figure a b c be a triangle; then will the sum of the angles a, b, and c, be equal to two right angles.

For, produce the side a c to d.

The new angle b c d is equal to the sum of the angles a and b.

If to the angles a and b we add the angle c, we shall have the three angles of the triangle.

If to the angle b c d we add the same angle c, we shall have the adjacent angles c and b c d.

Then the three angles of the triangle a, b, c, are equal to the adjacent angles c and b c d.

But the adjacent angles c and b c d are equal to two right angles.