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

If it were less, where would the line fall?

Why does the line d e fall exactly upon the line a b?

DEMONSTRATION.

We wish to prove that,

If two triangles have two angles, and the included side of the one equal to two angles and the included side of the other, each to each, the two triangles are equal to each other in all respects.

Let the triangles a b c and d e f have the angle b of the one equal to the angle e of the other; the angle c of the one equal to the angle f of the other; and the included side b c of the one equal to the included side e f of the other, each to each; then will the two triangles be equal in all their parts.

For place the triangle d e f upon the triangle a b c, so that the line e f shall fall upon the line b c, with the point e upon the point b.

Because the line e f is equal to the line b c the point f will fall upon the point c.

Because the angle e is equal to the angle b, the line e d will fall upon the line b a, and the point d will be somewhere in the line b a.