 | Yale University - 1898 - 212 pages
...the surface and volume, respectively, of the cube. JUNK 1895. PLANE. 1. If two sides of a triangle are unequal, the angles opposite are unequal, and the greater angle is opposite the greater side. Also state and prove the converse proposition. 2. Define a locus. Find the locus of the centers of... | |
 | Webster Wells - Geometry - 1898 - 284 pages
...since Z ABC is > Z ABD, and v PROP. XXXIII. THEOREM. 99. (Converse of Prop. XXXII.) If two angles of a triangle are unequal, the sides opposite are unequal, and the greater side lies opposite the greater angle. J> Given, in A ABC, Z ABC >ZC To Prove AC>AB. Proof. Draw line BD,... | |
 | George Albert Wentworth - Geometry - 1898 - 462 pages
...angles are 70°, 75°, and 95° ; find the sides of its polar triangle. PROPOSITION XXV. THEOREM. 756. If two angles of a spherical triangle are unequal, the sides opposite an unequal, and the greater side is opposite the greater angle; CONVERSELY/Z/ two sides are unequal,... | |
 | William James Milne - Geometry - 1899 - 398 pages
...sides are unequal. How do the angles opposite these sides compare? Which one is the greater? Theorem. If two angles of a spherical triangle are unequal,...and the greater angle is opposite the greater side. . Data: A spherical triangle, as ABC, in j / which the angle ACB is greater than the tL^L^ ^4 angle... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...of Z t7, and AC of Z 5'. (?) .-. AB = AC. ? (§ 593) (§ 31, 2) (§ 610) PROP. XXVII. THEOREM. 613. If two angles of a spherical triangle are unequal,...the sides opposite are unequal, and the greater side lies opposite the greater angle. Given, in spherical A ABC, Z ABC > Z C. To Prove AC > AB. (Prove by... | |
 | William James Milne - Geometry, Modern - 1899 - 258 pages
...the greater angle ? 2. Which side of a right triangle is the greatest? Theorem. If two angles of a triangle are unequal, the sides opposite are unequal,...and the greater side is opposite the greater angle. (Converse of Prop. XXVIII) Data: Any triangle, as ABC, in which angle ABC is greater than angle A.... | |
 | William James Milne - Geometry - 1899 - 404 pages
...the greater angle ? 2. Which side of a right triangle is the greatest ? ^ Theorem. If two angles of a triangle are unequal, the sides opposite are unequal,...and the greater side is opposite the greater angle. (Converse of Prop. XXVIII) Data: Any triangle, as ABC, in which angle ABC is greater than angle A.... | |
 | George Albert Wentworth - Geometry, Plane - 1899 - 278 pages
...each of the two remaining angles ? PROPOSITION XXVII. THEOREM. 153. RECIPROCALLY : If two angles of a triangle are unequal, the sides opposite are unequal,...and the greater side is opposite the greater angle. In the triangle ACB, let the angle C be greater than the angle B. To prove that AB > A C. Proof. Now... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...hypotenuse and an acute Z of the other). QED PROPOSITION XXVI. THEOREM. 152. If two sides of a triangle are unequal, the angles opposite are unequal, and the greater angle is opposite the greater side. c B In the triangle ACB, let AB be greater than AC. To prove that ZA CB is greater than Z B. Proof.... | |
 | Education - 1900 - 612 pages
...are either equal or supplementary. Give proof for both cases. 3 Prove that if two sides of a triangle are unequal the angles opposite are unequal and the greater angle is opposite the greater side. 4 Prove that an angle formed by two chords intersecting within the circumference is measured by one... | |
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If two angles of a spherical triangle are unequal, the sides opposite are unequal,, and the greater side is opposite the greater angle... 
