 | Edward Olney - Geometry - 1879 - 502 pages
...trirectangular triangle, is equilateral and Us sidet are quadrants. PROPOSITION XT. 579. Theorem. — In an isosceles spherical triangle the angles opposite the equal sides are equal ; and, conversely, If ttoo angles of a spherical triangle are equal, the triangle is isosceles. DEM.... | |
 | Edward Olney - Geometry - 1882 - 262 pages
...The trirectangular triangle is equilateral and its sides are quadrants. PROPOSITION XV. Theorem. — In an isosceles spherical triangle the angles opposite the equal sides are equal ; and, conversely, If two angles of a spherical triangle are equal, the triangle is isosceles. DEM.—... | |
 | Franklin Ibach - Geometry - 1882 - 208 pages
...angle of the other. ВЕЪАТКШ BETWEEN THE PARTS OF A TRIANGLE. THEOREM XXXI. 94. In an isosceles triangle, the angles opposite the equal sides are equal. In the isosceles A ABC, let AC and B С be the equal sides. С ADB To prove that ¿- a = ¿- b. Let CD be drawn to the... | |
 | Edward Olney - Geometry - 1883 - 352 pages
...be a spherical triangle whose sides are 52°, 126°, and 140°? PROPOSITION XVIII. 699. Theorem. — In an isosceles spherical triangle, the angles opposite the equal sides are equal; and, conversely, // two angles of a spherical triangle are equal, the triangle is isosceles. DEMONSTRATION.... | |
 | Edward Olney - Geometry - 1883 - 344 pages
...31° ? Can there be one whose sides are 152°, 136°, 148° ? PROPOSITION XVIII. 699. Theorem.—In an isosceles spherical triangle, the angles opposite the equal sides are equal; and, conversely, // two angles of a spherical triangle are equal, the triangle is isosceles. DEMONSTRATION.... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...tri-rectangular triangles (§§ 650, 676), ABC, A'BC, AB'C, etc. 334 PROPOSITION XX. THEOREM. 679. Jn an isosceles spherical triangle the angles opposite the equal sides are equal. In the spherical triangle ABC, let AB = AC. To prove that Z. B = Z C. Let AD be an arc of a great circle bisecting... | |
 | William Chauvenet - Geometry - 1887 - 336 pages
...the two triangles will then be similar, as in the case of plane triangles. EXERCISES. 1. Theorem. — In an isosceles spherical triangle the angles \ opposite the equal sides are equal. 2. Theorem. — The arc drawn from the vertex of an isosceles spherical triangle to the middle point... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 336 pages
...two triangles will then be similar, as in the case of plane triangles. EXERCISES. 1. Theorem.—In an isosceles spherical triangle the angles opposite the equal sides are equal. 2. Theorem.—The arc drawn from the vertex of an isosceles spherical triangle to the middle point... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...two triangles will then be similar, aQ in the case of plane triangles. EXERCISES. 1. Theorem.—In an isosceles spherical triangle the angles opposite the equal sides are equal. 2. Theorem.—The arc drawn from the vertex of an isosceles spherical triangle to the middle point... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...and equal or symmetrical. (706) . • . they are either equal or equivalent. (708) QED 712. COR. 1. In an isosceles spherical triangle, the angles opposite the equal sides are equal. For, in the A ABC, let AB - AC ; pass the arc AD of a great O through A and the mid. pt. of BC ; then... | |
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In an isosceles spherical triangle, the angles opposite the equal sides are equal. In the spherical triangle ABC, let AB equal AC. 
