CHAPTER I 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 motion.1 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. 1 But see the footnote to 3.–transl. 9

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