 | Edward Olney - Geometry - 1872 - 472 pages
...formed by any side with its adjacent side produced, as CBD, Fig. 174. PROPOSITION IT* 231. TJteorem. — An exterior angle of a triangle is equal to the sum...triangle, and CBD an exterior angle; then CBD = A + C. For CBD is the supplement of CBA by (131), and CBA is the supplement of A + C by (221). Hence,... | |
 | L J V. Gerard - 1874 - 428 pages
...ABC [II. 21]: therefore the three angles are together equal to two right angles, WWTBD COROLLARY I. An exterior angle of a triangle, is equal to the sum of the two oppositeinterior angles. COROLLARY II. If two angles of a triangle be equal to two angles of... | |
 | Edward Olney - Geometry - 1877 - 272 pages
...formed by any side with its adjacent side produced, as CBD, Fig. 174. PROPOSITION IV. 231. Theorem. — An exterior angle of a triangle is equal to the sum of the two interior non-adjacent angles. . 174. DEM. — Let ABC be any triangle, and CBD an exterior angle; then CBD = A + C. For CBD is the... | |
 | Edward Olney - Geometry - 1879 - 502 pages
...is an angle formed by any side with its adjacent side produced, as CBD, Fig. 174. i PROPOSITION IV. 231. TJieorem. — An exterior angle of a triangle...triangle, and CBD an exterior angle; then CBD = A + C. For CBD is the supplement of CBA by (131), and CBA is the supplement of A + C by (221). Hence,... | |
 | Edward Olney - Geometry - 1883 - 352 pages
...formed by any side with its adjacent side produced, as CBD, Fig. 116. PROPOSITION IV. Theorem.— Any exterior angle of a triangle is equal to the sum of the two interior non-adjacent angles. DEMONSTRATION. Let ABC be a triangle, and CBD be an exterior angle. We are to prove that CBD = A +... | |
 | Richard Wormell - Geometry, Plane - 1883 - 210 pages
...Construct a triangle, having given the sum of bvo angles and the sides opposite to them. The fact that the exterior angle of a triangle is equal to the sum of the two interior and opposite angles suggests the following construction : Make A С D equal to the given sum, and produce... | |
 | George Albert Wentworth - 1884 - 264 pages
...equal. 31. Corollary II. The sum of the acute angles of a right triangle is equal to 90°. 32. Theorem. An exterior angle of a triangle is equal to the sum of the two opposite interior angles. 33. Theorem. The sum of the angles of a quadrilateral is equal to... | |
 | George Bruce Halsted - Geometry - 1885 - 389 pages
...parallel to the same line cannot intersect, and so are parallel to one another, THEOREM XXI. 173. Each exterior angle of a triangle is equal to the sum of the two interior opposite angles. HYPOTHESIS. ABC any A, with side AB produced to D. CONCLUSION. £ CBD = 4 A + 4 C.... | |
 | William Kingdon Clifford - Mathematics - 1885 - 310 pages
...Fio. 21. The other form into which our proposition may be thrown is that either of the exterior angles of a triangle is equal to the sum of the two interior angles opposite to it. For, in the figure, the exterior angle A c D, together with A c B, makes two... | |
 | George Bruce Halsted - Geometry - 1886 - 394 pages
...parallel to the same line cannot intersect, and so are parallel to one another. THEOREM XXI. 173. Each exterior angle of a triangle is equal to the sum of the two interior opposite angles. HYPOTHESIS. ABC any A, with side AB produced to D. CONCLUSION. £ CBD = £A + 4 C.... | |
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The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. 
