T
H
E

E
L
E
M
E
N
T
S
Book I   Proposition 12
For, since GH is equal to HE, and HC is common,
    the two sides GH, HC are equal to the two sides EH, HC respectively; and the base CG is equal to the base CE;

therefore
    the angle GHC is equal to the angle EHC. [I.8]

And they are adjacent angles.
    But, when a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands. [Def.10]
Previous Page    Return to Propositions    Next Page