On Angles
10. The figure formed by two rays issuing from the same endpoint is called an
angle. The point is called the vertex of the angle, and the two rays are its sides.
Figure 7
We denote an angle by the letter of its vertex, placed between two other letters
which indicate the sides, often surmounted by a special symbol. If, however, the
figure contains only one angle with the vertex considered, that letter will suffice to
designate the angle. Thus, the angle formed by the two rays AB, AC (Fig. 7) will
be denoted by BAC or, more simply, by A.
Two angles are said to be congruent, in agreement with the definition of con-
gruent figures (3) if they can be superimposed by a rigid
Figure 8
Figure 9
Two congruent angles, BAC, B A C , can be superimposed in two different
ways: namely, either AB takes the direction of A B and AC the direction of A C ,
or the other way around. We pass from one to the other by turning the angle
around onto itself, for instance, by moving the angle BAC in such a way that AC
occupies the position previously occupied by AB, and vice-versa.
see the footnote to 3.–transl.
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