 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
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...the same order or in opposite orders. Compare Article 467, or prove by superposition. EXERCISES 1. If two angles of a spherical triangle are equal, the sides opposite those angles are also equal. 2. The arcs of great circles which bisect the angles of a spherical triangle... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...Ex. 1199. A tri.rectangular triangle is equal to its polar triangle. PROPOSITION XVII. THEOREM 737. If two angles of a spherical triangle are equal, the sides opposite are equal. Proof. Construct polar A A'B'C'. Then A'B' is the supplement of ZC, and A'C' the supplement... | |
 | George Albert Wentworth - Geometry, Solid - 1902 - 248 pages
...angles are 70°, 75°, and 95°. Find the sides of its polar triangle. PROPOSITION XXIII. THEOREM. 814. If two angles of a spherical triangle are equal, the...these angles are equal and the triangle is isosceles. In the spherical triangle ABC, let the angle B equal the angle C. To prove that AC = AB. Proof. Let... | |
 | Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...the spherical A ABC in which AB — AC. To prove /.B=/.C. Proof. Draw an arc from the vertex A to D, the midpoint of the base. Let the pupil supply the...two angles of a spherical triangle, are equal, the aides opposite these angles are equal, and the triangle is isosceles. .A i B' / -6' Given the spherical... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...Find the sides of its polar triangle. . BOOK VIII. SOLID GEOMETRY. PROPOSITION XXIII. THEOREM. 814. If two angles of a spherical triangle are equal, the...these angles are equal and the triangle is isosceles. In the spherical triangle ABC, let the angle B equal the angle C. To prove that AC = AB. Proof. Let... | |
 | Joseph Claudel - Mathematics - 1906 - 758 pages
...angles B and C opposite the equal sides are equal ; and conversely, if in a triangle two angles B and C are equal, the sides opposite these angles are equal and the triangle is isosceles. In an isosceles trill nc angle the altitude Am bisects the angle A and the Fig. a> base BC (639). 636.... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...813 In an isosceles spherical triangle, the angles opposite the equal sides are equal ; conversely, if two angles of a spherical triangle are equal, the sides opposite are equal, and the triangle is isosceles. Fig. 1 Fig. 2 HYPOTHESIS. In the spherical A ABC, AB = AC... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...813 In an isosceles spherical triangle, the angles opposite the equal sides are equal ; conversely, if two angles of a spherical triangle are equal, the sides opposite are equal, and the triangle is isosceles. Fig. 1 Fig. 2 HYPOTHESIS. In the spherical A ABC, AB = AC... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...midpoint of the base bisects the vertex. angle and is perpendicular to the base. (See 749.) 770. THEOREM. If two angles of a spherical triangle are equal, the sides opposite are equal. Given: (?). To Prove : (?). Proof: Construct A A'B'C', the polar triangle of A ABC. Then,... | |
 | Webster Wells - Geometry - 1908 - 336 pages
...triangle which is symmetrical to it. For the equal parts occur in the same order. PROP. XX. THEOREM 562. If two angles of a spherical triangle are equal, the sides opposite are equal. (Converse of Prop. XIX.) Given in spherical A ABC, ZB = Z C. To Prove AB = AC. Proof. 1.... | |
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