 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...of a quadrilateral is less than one half the perimeter of the figure. PROPOSITION XXIX. THEOREM 128. If two sides of a triangle are unequal, the angles...and the greater angle is opposite the greater side. Given A ABC, with To prove E AC>AB. C. Proof STATEMENTS Draw the angle.bisector AE. On AC lay off AD... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...of a quadrilateral is less than one half the perimeter of the figure. PROPOSITION XXIX. THEOREM 128. If two sides of a triangle are unequal, the angles...and the greater angle is opposite the greater side. 8" Given A ABC, with To prove AC>AB. C. Proof STATEMENTS Draw the angle.bisector AE. On AC lay off... | |
 | David Eugene Smith - Geometry, Solid - 1924 - 256 pages
...external point is the perpendicular from the point to the line. 15. Inequalities in Relation to Triangles. 1. If two sides of a triangle are unequal, the angles opposite these sides are unequal, and the angle opposite the greater side is the greater. 3. If two sides of... | |
 | Julius J. H. Hayn - Geometry, Plane - 1925 - 328 pages
...Construction of a parallel depending on only one intersection of arcs. Exercises Group 42 120. Prop. XLVI. If two sides of a triangle are unequal, the angles...and the greater angle is opposite the greater side. 119. Two sides and an angle opposite one of them. 121. Prop. XLVII. If two angles of a triangle are... | |
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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. 
