| Engineering - 1884 - 620 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), Fig.2 "Turn the triangle ABC over, and suppose it to take... | |
| George Bruce Halsted - Geometry - 1885 - 389 pages
...PROOF. By 133, from a cut off BD = c. By 100, join AD. Then, because BD = c, :. £ BDA = £ BAD. (126. **In an isosceles triangle the angles opposite the equal sides are equal.)** And, by 142, the exterior ^ BDA of A CD A > the opposite interior ^ C, :. also £ BAD >£C. Still more... | |
| Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...respects, the equal sides lie opposite the equal angles ; and conversely. PROPOSITION XI. THEOREM. **In an isosceles triangle the angles opposite the equal sides are equal.** BOOK I. Join the vertex A and the middle point D of the base BC. Then, AB is equal to AC, by hypothesis,... | |
| Webster Wells - Geometry - 1886 - 392 pages
...obtuse-angled triangle the sum of the acute angles is less than a right angle. PROPOSITION XXV. THEOREM. 89. **In an isosceles triangle the angles opposite the equal sides are equal.** DB Let ABC be an isosceles triangle in which AC and BC are the equal sides. To prove that ZA = Z B.... | |
| George Bruce Halsted - Geometry - 1886 - 394 pages
...£ACB, (168. If a transversal cuts two parallels, the alternate angles are equal.) 4 ACB = 4 ABC, (126. **In an isosceles triangle the angles opposite the equal sides are equal.)** 4 ABC = 4 DAN, (169. If a transversal cuts two parallels, the corresponding angles are equal.) (128.... | |
| William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...the one are respectively equal to a side and the two adjacent angles of the other. PROPOSITION VIII. **In an isosceles triangle the angles opposite the equal sides are equal.** Corollary. The straight line bisecting the vertical angle of an isosceles triangle bisects the base,... | |
| William Chauvenet - Geometry - 1887 - 336 pages
...the one are respectively equal to a side and the two adjacent angles of the other. PROPOSITION VIII. **In an isosceles triangle the angles opposite the equal sides are equal.** Corollary. The straight line bisecting the vertical angle of an isosceles triangle bisects the base,... | |
| George Anthony Hill - Geometry - 1888 - 200 pages
...because the same reasoning will hold good for any two triangles that can be drawn. • 4. Theorem. — **In an isosceles triangle the angles opposite the equal sides are equal.** HYPOTHESIS. ABC an isosceles triangle. AC and BC the equal sides. CONCLUSION. ADB PROOF. Successive... | |
| George Anthony Hill - Geometry - 1888 - 202 pages
...because the same reasoning •will hold good for any two triangles that can be drawn. 4. Theorem. — **In an isosceles triangle the angles opposite the equal sides are equal.** HYPOTHESIS. ABC an isosceles triangle. AC and BC the equal sides. CONCLUSION. ZABC = ZBAC. ADD PROOF.... | |
| George Albert Wentworth - Geometry - 1888 - 264 pages
...equal Z D, and is not less than Z D. .-, Z A is greater than Z D. QEO PROPOSITION XXIX. THEOREM. 154. **In an isosceles triangle the angles opposite the equal sides are equal.** A Let ABC be an isosceles triangle, having the sides AB and AC equal. To prove Z 11 =•- Z C. Proof.... | |
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