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

As the line d f is equal to the line a c, upon what point will the point f fall?

Then, if the point e falls upon the point b, and the point f upon the point c, where will the line e f fall?

Now, because the three sides of the triangle d e f exactly fall upon the three sides of the triangle a b c, we say the two magnitudes coincide throughout their whole extent, and are therefore equal.

What three parts of the triangle a b c did we suppose to be equal to three corresponding parts of the triangle d e f before we placed one upon the other.

What line of the one do we find equal to a line in the other?

What two angles of the one do we find equal to two angles in the other?

What do you think of the areas of the triangles?

DEMONSTRATION.

We wish to prove, that,