 | 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,... | |
 | 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... | |
 | 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.... | |
 | 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.... | |
 | 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 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.... | |
 | 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 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 Albert Wentworth - 1889 - 264 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... | |
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In an isosceles triangle, the angles opposite the equal sides are equal. Let ABC be an isosceles triangle, in which the side AB is equal to the side AC ; then will the angle B be equal to the angle C. 
