 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...opposite to equal sides. THEOREM. 483. In every isosceles spherical triangle Hie angles opposite to the equal sides are equal ; and conversely, if two angles of a spherical triangle are equal, the triangle is isosceles. Demonstration. 1. Let AB be equal AC (fig.... | |
 | Adrien Marie Legendre - Geometry - 1822 - 394 pages
...equal. In the same manner it may be shewn, that B is equal to E, and C to F. PROPOSITION XII. THEOREM. In an isosceles triangle, the angles opposite the equal sides are equal. LET the side AB be equal to AC, the angle C will be equal to B. Join A the vertex, and D the middle... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...opposite to equal sides. THEOREM. 483. In every isosceles spherical triangle the angles opposite to the equal sides are equal ; and conversely, if two angles of a spherical triangle are equal, the triangle is isosceles. Demonstration. 1. Let jJD be equal to AC (fig.... | |
 | Adrien Marie Legendre - Geometry - 1825 - 276 pages
...opposite to equal sides. THEOREM. 483. In every isosceles spherical triangle the angles opposite to the equal sides are equal ; and conversely, if two angles of a spherical triangle are equal, the triangle is isosceles. Demonstration. 1. Let AB be equal to AC (Jig.... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...thus, the equal angles D and A, lie opposite the equal sides EF and BC. . PROPOSITION XI. THEOREM. In an isosceles triangle, the angles opposite the equal sides are equal. Let the side BA be equal to the side AC ; then will the angle C be equal to the angle B. For, join... | |
 | Benjamin Peirce - Geometry - 1837 - 216 pages
...eqnnl to those of another, the other sides and angle are also equal in the two triangles. 55. Theorem. In an isosceles triangle the angles opposite the equal sides are equal. Equal Angles of the Isosceles Triangle. Demonstration. In the isosceles triangle ABC (fig. 32), let... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...opposite to equal sides. THEOREM. 483. In every isosceles spherical triangle the angles opposite to the equal sides are equal ; and conversely, if two angles of a spherical triangle are equal, tfie triangle is isosceles. Demonstration. 1. Let AB be equal to AC (fig.... | |
 | Nicholas Tillinghast - Geometry, Plane - 1844 - 110 pages
...and DF be equal to AC, EF equal to BC, and the angle at F equal to the angle atC. PROP. VI. THEOREM. In an isosceles triangle, the angles opposite the equal sides are equal. Fig. 6. 11 Let AB, BC, be the equal sides ; then we have to prove that the angle A is equal to £_... | |
 | Nathan Scholfield - Conic sections - 1845 - 244 pages
...must be equal, and lie opposite to equal sides. PROPOSITION XV. THEOREM. In every 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. First. Suppose the side AB=AC; we shall have... | |
 | Nathan Scholfield - 1845 - 894 pages
...must be equal, and lie opposite to equal sides. PROPOSITION XV. THEOREM. In every 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. First. Suppose the side AB=AC; we shall have... | |
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In an isosceles triangle the angles opposite the equal sides are equal. 
