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

For, draw the diagonal b d.

Because the figure is a parallelogram, the sides a b and d c are parallel, and the interior alternate angles n and o are equal.

Because the figure is a parallelogram, the interior alternate angles r and m are equal.

Then the two triangles a d b, b d c, have two angles and the included side of the one equal to two angles and the included side of the other, each to each, and are therefore equal;

And the side a b opposite the angle m is equal to the side c d opposite the equal angle r;

And the side a d opposite the angle n is equal to the side b c opposite the equal angle o.

TEST.

Prove the same by drawing a diagonal from a to c.

PROPOSITION XVI. THEOREM.