 If two angles of a spherical triangle are equal, the sides opposite these angles are equal and the triangle is isosceles. Given the spherical triangle ABC, with angle B equal to angle C. To prove that AC = AB. Proof. Let A A'B'C ' be the polar triangle...  Plane and Solid Geometry - Page 450by Fletcher Durell - 1911 - 546 pagesFull view - About this book
 | Mabel Sykes, Clarence Elmer Comstock - Geometry, Modern - 1918 - 576 pages
...circle. Prove ZA and ZB corresponding angles of symmetric spherical triangles (Fig. 122). THEOREM 93. If two angles of a spherical triangle are equal, the sides opposite the equal angles are equal (Fig. 122). Analysis: To prove AC= CB, prove that A A' and B' of the polar... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...1690. A tri-rectangular triangle is congruent to its polar triangle. PROPOSITION XVIII. THEOREM 760. If two angles of a spherical triangle are equal, the sides opposite are equal. Given spherical triangle ABC\ with Z. B — ZC To prove AB —AC. Proof. Construct polar... | |
 | Charles Austin Hobbs - Geometry, Solid - 1921 - 216 pages
...mid-point of base bisects the vertical angle and is perpendicular to the base. * Proposition 337 Theorem // two angles of a spherical triangle are equal, the...these angles are equal, and the triangle is isosceles. HINT. Construct the polar A of the given A, and consult Prop. 329 and Prop. 336. * Proposition 338... | |
 | Clarence Addison Willis - Geometry, Modern - 1922 - 318 pages
...order as that of the sides to which they are opposite (109). 130. Theorem XI.—// two angles of a triangle are equal, the sides opposite these angles are equal and the triangle is isosceles (108). Helps.—Draw the triangle with two equal angles. Draw an auxiliary line bisecting the third... | |
 | Mabel Sykes, Clarence Elmer Comstock - Geometry, Solid - 1922 - 236 pages
...circle. Prove LA and ZB corresponding angles of symmetric spherical triangles (Fig. 122). THEOREM 93. If two angles of a spherical triangle are equal, the sides opposite the equal angles are equal (Fig. 122). Analysis: To prove AC = CB, prove that A A' and B' of the polar... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...angles of a spherical quadrilateral is greater than four right angles. PROPOSITION XVIII. THEOREM 760. If two angles of a spherical triangle are equal, the sides opposite are equal. Given spherical triangle ABC, with Z. B = ZC To prove AB = AC. Proof. Construct polar A... | |
 | David Eugene Smith - Geometry, Solid - 1924 - 256 pages
...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 AC = AB. Prove that ZB = Z C. Proof. Let... | |
 | Julius J. H. Hayn - Geometry, Plane - 1925 - 328 pages
...coincide, and are equal. QED 100 PLANE GEOMETRY Proposition XXXIII. Theorem 98. // two angles of a triangle are equal, the sides opposite these angles are equal, and the triangle is isosceles. Student, make up hypothesis and determination. Hints: Let CE be the bisector of angle ACB, then angles... | |
 | National Committee on Mathematical Requirements - Mathematics - 1927 - 208 pages
...[73*] If two sides of a spherical triangle are equal, the angles opposite these sides are equal. [84] If two angles of a spherical triangle are equal, the sides opposite these angles are equal. [85] If two angles of a spherical triangle are unequal, the sides opposite these angles are unequal,... | |
 | Education - 1896 - 606 pages
...line only one perpendicular can be erected to the line. Demonstrate. 3. If the opposite angles of a triangle are equal the sides opposite these angles are equal and the triangle is isosceles. Demonstrate. 4. The bisector of an angle of a triangle divides the opposite side into segments proportional... | |
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