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

PROPOSITION XIII. THEOREM.

DEVELOPMENT LESSON.

In these two triangles we have tried to make the side a b of the one equal to the side d e of the other; the side a c of the one equal to the side d f of the other; and the included angle b a c of the one equal to the included angle e d f of the other.

We now wish to find out if the third side b c of the one is equal to the third side e f of the other, and if the two remaining angles b and c of the one are equal to the two remaining angles e and f of the other.

Suppose we were to cut the triangle d e f out of the page, and place it upon the triangle a b c, so that the line d e should fall upon the line a b, and the point d upon the point a.

As the line d e is equal to the line a b, upon what point will the point e fall?

If the angle e d f were less than the angle b a c, would the line d f fall within or without the triangle?

If the angle e d f were greater than the angle b a c, where would the line d f fall?

Since the angle a is equal to d, where, then, must the line d f fall?