By Slaught, H. E. (Herbert Ellsworth) ; Lennes, N. J. (Nels Johann)

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Ill, § 61) (Ax. VII, §82) // in two triangles two' sides of the two sides the first is greater of the other but the third side than the third side of the second, then the included angle of the first is greater than the included angle of the second. Suggestion. that Using the AOA'c', show figure of § 117 and the hypothesis that two of the three following statements are impossible: (1)ZB = ZB'; (2)Zb

A', AB=A'^. We are to show that A ABC ^ A a'b' c' Place A ABC upon AA'b'c' so that AB and . equal A'b' making C its , Then AC will take fall coincides with on the same side of a'b' as C'. A', on the ray a'c'. ), and on the ray B'c'. Since the point C lies on both of the rays A'cf and b'c', it must lie at their point of intersection c' (§ 5). Hence, the triangles coincide and are, therefore, congruent (§ "27). Also BC will take the direction of hence C must lie r EXERCISES. 36. 1. Tn the figure of § '^o is out of the plane in l\ABC lie?

And Is it Is any n ? l C? equal radii for both, that the point BA is EXERCISES. 49. 1. D. a In that case does the ray m usiiii;- the angle By means of § 48 bisect a straight angle. \\'hat is the ray called a straight angle? In this case what restriction is necessary on the radii used for the arcs m and n 3. which bisects '! 4. By Ex. 5. Construct a perpendicular to a segment 3 construct a perpendicular to a line at a given point in at one end of it it. without prolonging the segment and without using the square ruler.