 | College Entrance Examination Board - Mathematics - 1915 - 72 pages
...in preparation GROUP A. (Answer four questions from this group.) 1. Complete this theorem and prove: If two sides of a triangle are unequal, the angles opposite are unequal, and the greater State the hypothesis of the above theorem. Point out where it is needed and used in your proof. State... | |
 | Webster Wells, Walter Wilson Hart - Geometry, Plane - 1915 - 330 pages
...greater than either remote interior angle of the triangle. (§ 87.) PROPOSITION XXXIII. THEOREM 161. If two sides of a triangle are unequal, the angles opposite are unequal, the angle opposite the greater side being the greater. Hypothesis. In A ABC, AC > AB. Conclusion. ZB... | |
 | John Wesley Young, Albert John Schwartz - Geometry, Modern - 1915 - 248 pages
...INEQUALITIES INEQUALITIES 210. THEOREM. If two sides of a triangle are unequal, the opposite angles are unequal, and the greater angle is opposite the greater side. Given the A ABC with CB > CA. To prove that ZA > Z B. Proof. 1. Draw CM bisecting Z <7and cutting AB in D.... | |
 | William Betz - Geometry - 1916 - 536 pages
...obtuse triangle the right or the obtuse angle is the greatest angle. PROPOSITION XXVIII. THEOREM 224. If two sides of a triangle are unequal, the angles...and the greater angle is opposite the greater side. A C Given the triangle ABC, in which AB is greater than AC. To prove that Z.ACB>/.B. Proof. 1. On AB... | |
 | William Betz, Harrison Emmett Webb - Geometry, Solid - 1916 - 214 pages
...the second, and the second is greater than the third, then the first is greater than the third. 224. If two sides of a triangle are unequal, the angles...and the greater angle is opposite the greater side. 225. If two angles of a triangle are unequal, the sides opposite are unequal, and the greater side... | |
 | Edith Long, William Charles Brenke - Geometry, Plane - 1916 - 292 pages
...exterior angle of a triangle is greater than either interior angle not adjacent to it. Theorem XII. If two sides of a triangle are unequal, the angles opposite are unequal, and the greater side has the greater angle opposite it. Part III. Transversals — Parallel lines — Sums of angles... | |
 | Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...exterior angle of a triangle is greater than either interior angle not adjacent to it. Theorem XII. If two sides of a triangle are unequal, the angles opposite are unequal, and the greater side has the greater angle opposite it. Part III. Transversals— Parallel lines — Sums of angles... | |
 | Webster Wells, Walter Wilson Hart - Geometry - 1916 - 490 pages
...greater than either remote interior angle of the triangle. (§ 87.) PROPOSITION XXXIII. THEOREM 161. If two sides of a triangle are unequal, the angles opposite are unequal, the angle opposite the greater side being the greater. Hypothesis. In A ABC, AC > AB. Conclusion. ZB... | |
 | John H. Williams, Kenneth P. Williams - Geometry, Solid - 1916 - 184 pages
...§797 But BD+DA >BA by § 742, and CA = BD+DA. Hence, CA>BA. QED 799. COR. // two sides of a spherical triangle are unequal, the angles opposite are unequal, and the greater angle lies opposite the greater side. 800. A spherical pyramid is the portion of a sphere bounded by a spherical... | |
 | Ernst Rudolph Breslich - Logarithms - 1917 - 408 pages
...circle making Then or AC<CD+DA, AC<CD+DB. .: Tc<CB. ' 229 348. Theorem: // two sides of a spherical triangle are unequal, the angles opposite are unequal and the greater angle lies opposite the greater side. Prove by the indirect method. 349. Theorem: The diameters of a sphere... | |
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If two sides of a triangle are unequal, the angles opposite are unequal, and the greater angle is opposite the greater side. 
