 | Michigan. Department of Public Instruction - Education - 1896 - 710 pages
...the sphere. 2. Demonstrate: 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. 3. (a) Can there be a spherical triangle whose sides are 78°, 113°, and 31°? Why? (b) Can there... | |
 | William Chauvenet - 1905 - 336 pages
...middle point of the base is perpendicular to the base, and bisects the vertical angle. 3. Theorem.—Tf two angles of a spherical triangle are equal, the triangle is isosceles. PROPOSITION XVI.—THEOREM. 61. Any side of a spherical triangle is less than the sum of the other... | |
 | Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...triangle to the midpoint of the base bisects the vertical angle and is perpendicular to the base. 6. If two angles of a spherical triangle are equal, the triangle is isosceles. SUGGESTION. Construct the polar triangle of ABC. Then A'B' = A'C'. Use Ex. 4, etc. 7. The sum of any... | |
 | George C. Shutts - 1913 - 212 pages
...given point? 89. The angles opposite the equal sides of an isosceles spherical triangle are equal. 90. If two angles of a spherical triangle are equal, the triangle is isosceles. 454 SOLID CiEOMETRY PROPOSITION XXIX. 752. THEOREM. The sum of the angles of a spherical triangle is... | |
 | Claude Irwin Palmer - Geometry, Solid - 1918 - 192 pages
...symmetric. EXERCISES 1. Is there a theorem in plane geometry analogous to the theorems of §§ 856, 857? 2. If two angles of a spherical triangle are equal, the triangle is isosceles. 3. If a spherical triangle is equiangular it is equilateral. 858. Theorem. The sum of the angles of... | |
 | Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - Geometry, Solid - 1922 - 216 pages
...Hence it is possible to construct only one triangle on a sphere whose angles are known. EXERCISES 78. If two angles of a spherical triangle are equal, the triangle is isosceles. 79. If the three angles of a spherical triangle are equal, the triangle is equilateral. 80. If two... | |
 | David Eugene Smith - Geometry, Solid - 1924 - 256 pages
...Isosceles Triangle 255. 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 sides opposite these angles are equal. \B Fig. 1 Fig. 2 1. Given the isosceles spherical A ABC with... | |
 | Harvard University - Education - 1874 - 378 pages
...cylinder, (3) parabolic cylinder. Prove that the bases of any cylinder are equal.3. Prove that when two angles of a spherical triangle are equal, the triangle is isosceles. ANALYTIC GEOMETRY. 1. Sketch rapidly the locus of the equation — + ?L = 1. Let the 25 9 unit be half... | |
 | Michigan. Legislature - Michigan - 1896 - 1090 pages
...the sphere. 2. Demonstrate: 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. 8. (a) Can there be a spherical triangle whose sides are 78°, 113°, and 31°? Why? (6) Can there... | |
 | Education - 1885 - 288 pages
...between the surfaceof a sphere and the convex surface of the circumscribing cj linder. 7. Prove that if two angles of a spherical triangle are equal, the triangle is isosceles. 8. State and demonstrate the limiting values of the sum of the angles of a spherical triangle. 9. Find... | |
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For, if the arc AD be drawn from the vertex A to the middle point D of the base, the two triangles ABD, ACD, will have all the sides of the one respectively equal to the corresponding sides of the other... 
