THEOREM 21. [Euc. I. 34.] The opposite sides and angles of a

parallelogram are equal to one another, and each diagonal

bisects the parallelogram.

CoR. 1. If one angle of a parallelogram is a right angle, all

its angles are right angles.

Cor. 2. All the sides of a square are equal ; and all its

angles are right angles.

COR. 3. The diagonals of a parallelogram bisect one

another.

THEOREM 22. If there are three or more parallel straight lines,

and the intercepts made by them on any transversal are equal,

then the corresponding intercepts on any other transversal

are also equal.

COR. In a triangle ABC, if a set of lines Pp, Qq, Rr, ...

drawn parallel to the base, divide one side AB into equal parts,

they also divide the other side AC into equal parts.

DIAGONAL SCALES