 | Isaac Newton Failor - 1906 - 440 sider
...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 - 1906 - 431 sider
...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 - 1907 - 428 sider
...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 - 1908 - 336 sider
...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.... | |
 | Fletcher Durell - 1911 - 234 sider
...Let the pupil supply the remainder of the proof. PROPOSITION XXI. THEOREM (CONY. OP PROP. XX) 800. If two angles of a spherical triangle are equal, the sides opposite these angles are equal, and the triangle is isosceles. Given the spherical A ABC in which ZB= Z 0.... | |
 | Clara Avis Hart, Daniel D. Feldman, Virgil Snyder - 1912 - 230 sider
...ABC, with side AB = side BO. To prove ZA = ZC HINT. Compare with § 111. PROPOSITION XIX. THEOREM 962. If two angles of a spherical triangle are equal, the sides opposite are equal. g ,"'$ Given spherical A BST with ZB = Z T. To prove r = t. ARGUMENT 1 Let A B's'T' be the... | |
 | Arthur Schultze, Frank Louis Sevenoak - 1913 - 490 sider
...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 AB C, with Z. B = Z C. To prove AB = AC. Proof. Construct polar... | |
 | George Albert Wentworth, David Eugene Smith - 1913 - 496 sider
...perpendicular to the base, and divides the triangle into two symmetric triangles. PROPOSITION XX. THEOREM 680. 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... | |
 | Sophia Foster Richardson - 1914 - 236 sider
...[Suggestion. Join the vertex to the midpoint of the base by the arc of a great circle.] 414. THEOREM. If two angles of a spherical triangle are equal, the sides opposite these angles are equal. [Suggestion. Construct the polar triangle of the given triangle and use §... | |
 | John Charles Stone, James Franklin Millis - 1916 - 196 sider
...the middle point of AJl. Compare A ADC and A DBCby § 481. Write the proof in full. 484. Theorem. — If two angles of a spherical triangle are equal, the sides opposite these angles are equal, and the triangle is isosceles. F Hypothesis. In spherical A ABC, ZA = Z B.... | |
| |
If two angles of a spherical triangle are equal, the sides opposite 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 the A A'B'C 
