Plane and solid geometry . 40 PLANE GEOMETRY Proposition VIII. Problem127. To construct the bisector of a given Given To construct the bisector of Z AB C. I. Construction 1. With B as center, and with any convenient radiuS;describe an arc intersecting BA at E and BC at D. 2. With D and E as centers, and with equal radii, describearcs intersecting at F, 3. Draw BF. 4. BF is the bisector of Z ABC. II. Proof Argument 1. In Aebf and FBD. BE = BD. 2. EF = DF, 3. 5F = Bi^. 4. ..AEBF=: AFBD. 6. Z J^B^ = Z /^J5Z). Reasons 1. By cons. 4. 2. By cons. 3. By A are equal if the thre
Plane and solid geometry . 40 PLANE GEOMETRY Proposition VIII. Problem127. To construct the bisector of a given Given To construct the bisector of Z AB C. I. Construction 1. With B as center, and with any convenient radiuS;describe an arc intersecting BA at E and BC at D. 2. With D and E as centers, and with equal radii, describearcs intersecting at F, 3. Draw BF. 4. BF is the bisector of Z ABC. II. Proof Argument 1. In Aebf and FBD. BE = BD. 2. EF = DF, 3. 5F = Bi^. 4. ..AEBF=: AFBD. 6. Z J^B^ = Z /^J5Z). Reasons 1. By cons. 4. 2. By cons. 3. By A are equal if the three sides of one areequal respectively to thethree sides of the other.§ parts of equalfigures are equal. § 110 5. HOOK I 41 Argument6. .*. BF is the bisector of/Labc. Reasons6. The bisector of an Z. isthe line which dividesthe Z. into two equalA. § 53. III. Discussion This construction is always possible, and there is only onesolution. Ex. 100. Draw an obtuse angle and divide it into: (a) fourequal angles ; (6) eight equal angles. Ex. 101. Construct the bisector of the vertex angle of an isosce
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