| Cornell University - 1880 - 868 pages
...tangent to a circle, the projection of one straight line upon another, four proportional magnitudes. 2. **In an isosceles triangle the angles opposite the equal sides are equal** to each other. Every equilateral triangle is also equiangular. An isosceles triangle is symmetric about... | |
| George Albert Wentworth - 1881 - 266 pages
...respectively to a side and two adj. A of the other). QED 111. COROLLARY. Two right triangles are equal when a **side and an acute angle of the one are equal respectively...to an homologous side and acute angle of the other.** TRIAXGLKS. PROPOSITION XXVIII. THEOREM. 112. In an isosceles triangle the angles opposite the equal... | |
| Simon Newcomb - Geometry - 1881 - 418 pages
...line. 90. Def. Segments of a straight line are the parts into which it is divided. • THEOREM IX. 91. **In an isosceles triangle the angles opposite the equal sides are equal** to cach other. Hypothesis. ABC a triangle in which CA = CB. Conclusion. Angle A = angle B. Proof. Bisect... | |
| George Albert Wentworth - Geometry, Plane - 1882 - 268 pages
...to a side and two adj. A of the other). QE D, 111. COROLLARY. Two right triangles are equal when a **side and an acute angle of the one are equal respectively...triangle the angles opposite the equal sides are equal.** E Let ABC be an Isosceles triangle, having the sides A С and С B equal. We are to prove Z. A = ZB... | |
| Franklin Ibach - Geometry - 1882 - 208 pages
...and an acute angle of the other. ВЕЪАТКШ BETWEEN THE PARTS OF A TRIANGLE. THEOREM XXXI. 94. **In an isosceles triangle, the angles opposite the equal sides are equal.** In the isosceles A ABC, let AC and B С be the equal sides. С ADB To prove that ¿- a = ¿- b. Let... | |
| Edward Olney - Geometry - 1883 - 354 pages
...chords are equal, the arcs are, and hence the angles subtended by these arcs. 223. COROLLARY 3. — **In an isosceles triangle the angles opposite the equal sides are equal** ; and, conversely, if two angles of a triangle are equal, the sides opposite are equal, and the triangle... | |
| Alfred Hix Welsh - Geometry - 1883 - 326 pages
...equal in all their parts (Th. IV)', and, consequently, the angle B is equal to the angle C. Therefore, **in an isosceles triangle, the angles opposite the equal sides are equal.** Cor. I.—An equilateral triangle is equiangular. For, if AB equals AC, then, by the Theorem just proved,... | |
| F. B. Stevens - Examinations - 1884 - 202 pages
...contained by the whole and one of the parts may be equal to the square on the other part. (LEGENDRE.) 1. **In an isosceles triangle the angles opposite the equal sides are equal.** 2. In equal circles, equal chords are equally distant from the centres ; and of two unequal chords... | |
| George Albert Wentworth - Geometry, Plane - 1884 - 266 pages
...each. 39. Corollary. Two right triangles are equal if their legs are equal, each to each. 40. Theorem. **In an isosceles triangle the angles opposite the equal sides are equal.** 41. Corollary. An equilateral triangle is equiangular. 42. Theorem. If in a triangle two angles are... | |
| W. Cain - 1884 - 156 pages
...any exterior angle is greater than either of the opposite interior, QED 35. We shall next show that, **In an isosceles triangle, the angles opposite the equal sides are equal.** In the triangle ABC, let AB = AC (Fig. 2), Turn the triangle ABC over, and suppose it to take the position... | |
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