Plane and solid geometry . 54 PLANE GEOMETRY Proposition XV. Theorem 156. If two sides of a triangle are unequal, the angleopposite the greater side is greater than the angle oppositethe less Given A ABC with BC >To prove Z CAB > Z (7. Argument 1. On BC lay off BD = AB, 2. Draw AD. 3. ThenZl = Z2. 4. NowZ2 > Za BA, 5. .-. Zl > Z C, 6. But Z CAB > Zl, 7. .-. /.CAB > Z a. Reasons 1. Circle post. §§ 122, 157. 2. Str. line post. I. § 54, 15. 3. The base A of an isosceles A are equal. § 111. 4. If one side of a A is pro- longed, the ext. Z formed > either of the r
Plane and solid geometry . 54 PLANE GEOMETRY Proposition XV. Theorem 156. If two sides of a triangle are unequal, the angleopposite the greater side is greater than the angle oppositethe less Given A ABC with BC >To prove Z CAB > Z (7. Argument 1. On BC lay off BD = AB, 2. Draw AD. 3. ThenZl = Z2. 4. NowZ2 > Za BA, 5. .-. Zl > Z C, 6. But Z CAB > Zl, 7. .-. /.CAB > Z a. Reasons 1. Circle post. §§ 122, 157. 2. Str. line post. I. § 54, 15. 3. The base A of an isosceles A are equal. § 111. 4. If one side of a A is pro- longed, the ext. Z formed > either of the remoteint. A. § 153. 5. Substituting Z 1 for its equal Z 2. 6. The whole > any of its parts. § 54, 12. 7. If three magnitudes of the same kind are so relatedthat the first > the sec-ond and the second >the third, then the first > the third. § 54, 10. 157. Note. Hereafter tliepostulates and definitions in full student will not be required to stateunless requested to do so by the teacher. BOOK I 55 158. Note. When two magnitudes are given unequal, tlie layingoff of the less upon the greater will often serve as the initial step in de-veloping a proof. Bx. 152. Given the isosce
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