 | Aaron Schuyler - Geometry - 1876 - 384 pages
...Proposition XXII.— Theorem. In a spherical triangle, the greater side is opposite the greater angle, and the greater angle is opposite the greater side. 1. In the triangle ABC, let .B > C; then, AC > AB. For, draw the arc BD of a great circle, making the angle CBD=BCD; then, DC =... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...C. Hence Z ABC is greater than Z C. PROPOSITION XXVIII. THEOREM. 95. CONVERSELY, if two angles of a triangle are unequal, the sides opposite are unequal, and the greater side lies opposite the greater angle. A In the triangle ABC let the angle ABC ber greater than the angle... | |
 | George Albert Wentworth - Geometry - 1888 - 264 pages
...equiangular triangle is also equilateral. PROPOSITION XXXI. THEOREM. 158. If two sides of a triangle are unequal, the angles opposite are unequal, and the greater angle is opposite the greater side. C u In the triangle ACB let AB be greater than AC. To prove Z A CB greater than Z B. Proof. Take AE... | |
 | George Albert Wentworth - Geometry - 1888 - 466 pages
...ratio of two homologous sides of these triangles. (See note, page 362.) PROPOSITION XXV. THEOREM. 756. If two angles of a spherical triangle are unequal,...greater side. 1 In the triangle ABC, let the angle ABC tie greater than the angle ACB. To prove AC>AB. Proof. Draw the arc BD of a great circle, making Z.... | |
 | George Albert Wentworth - Geometry - 1892 - 468 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,...is opposite the greater angle; CONVERSELY, if two aides are unequal, the angles opposite are unequal, and the greater angle is opposite the greater side.... | |
 | Examinations - 1893 - 408 pages
...radius is 4 feet. (Obtain result correct to two places of decimals.) 3 4 Prove that if two angles of a triangle are unequal, the sides opposite are unequal...and the greater side is opposite the greater angle. 5 5 Prove that an angle formed by a tangent and a secant intersecting without a circle is measured... | |
 | George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...either equal or supplementary. Define supplementary angles. 2. Prove that if two sides of a triangle are unequal, the angles opposite are unequal, and the greater angle is opposite the greater side. Define the various kinds of triangles. 3. Prove that in the same or equal circles equal chords are... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...angles opposite are unequal, and the greater angle is opposite the greater side. 159. If two angles of a triangle are unequal, the sides opposite are unequal,...and the greater side is opposite the greater angle. 160. Two triangles are equal if the three sides of the one are equal respectively to the three sides... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...hypothesis that angle b — angle c. Hence AC=AB. QE D / PROPOSITION XXI. THEOREM VS. If two angles of a triangle are unequal, the sides opposite are unequal,...and the greater side is opposite the greater angle. [Converse of Proposition XIX.] GIVEN in the triangle ABC, the angle a > angle c. To PROVE side ^C>side... | |
 | Mathematics - 1898 - 228 pages
...the surface and volume, respectively, of the cube. ' JUNE 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... | |
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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... 
