 If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.  The Element of Geometry - Page 13by John Playfair - 1836 - 114 pagesFull view - About this book
 | Woolwich roy. military acad, Walter Ferrier Austin - 1880 - 190 pages
...side, and the difference of the other two sides. 2. If a side of any triangle be produced, prove that the exterior angle is equal to the two interior and opposite angles, and that the three interior angles of every triangle are equal to two right angles. State and prove also... | |
 | 1880 - 186 pages
...use to which it is put, and where it is manufactured. EUCLID. (OPTIONAL.)—Time allowed If hoar. 1. If a side of any triangle be produced, the exterior angle is eqiul to the two interior and opposite angles ; and the three interior angles of every triangle are... | |
 | Herbert Spencer - 1881 - 752 pages
...case. therefore also the angles CBA, BAG, ACB, are together equal to two right angles. " Therefore if a side of any triangle be produced, the exterior...angles of every triangle are equal to two right angles. QED" Thus in each step by which the special conclusion is reached, as well as in the step taken from... | |
 | John Gibson - 1881 - 302 pages
...equal, each to each, and also the third angle of the one equal to the third angle of the other. 4. If a side of any triangle be produced, the exterior...and the three interior angles of every triangle are together equal to two right angles. 5. Describe a parallelogram that shall be equal to a given triangle... | |
 | Education, Higher - 1883 - 536 pages
...less than the other two sides of the triangle, but shall contain a greater angle. 6. If a side of a triangle be produced, the exterior angle is equal...angles of every triangle are equal to two right angles. Explain the term corollary. Enunciate and prove corollaries to the above. 7. The straight line joining... | |
 | Herbert Spencer - 1881 - 756 pages
...foregoing theorem is inconveniently long. We shall find a fitter one in Proposition xxxii. " If the side of any triangle be produced, the exterior angle...and the three interior angles of every triangle are together equal to two right angles. " Let ABC be a triangle, and let one of its sides BC be produced... | |
 | Moffatt and Paige - 1881 - 176 pages
...understood abbreviations for words may be used, but not symbols of operations, such as - , +, x .] 1. If a side of any triangle be produced, the exterior...opposite angles ; and the three interior angles of ev«*y triangle are together equal to two right angles. The base angle of an isosceles triangle is... | |
 | Education, Higher - 1884 - 538 pages
...segments of the circle. 9. Inscribe an equilateral asd equiangular quindecagon in a given circle. 10. If a side of any triangle be produced, the exterior...opposite angles, and the three interior angles of any triangle are together equal to two right angles. 11. The straight lines bisecting the angles at... | |
 | Euclides - Euclid's Elements - 1881 - 236 pages
...through the same point, the least is that whose base is bisected in that point. PROP. XXXII. THEOREM. If a side of any triangle be produced, the exterior...interior and opposite angles ; and the three interior anglet oj every triangle are together equal to two right angles. Let ABC be a triangle, and ).3t one... | |
 | Mary W I. Shilleto - 1882 - 418 pages
...In Euclid's figure for this proposition, if BG, CF meet in H, show that AH bisects the angle BAG. 2. If a side of any triangle be produced, the exterior...angles of every triangle are equal to two right angles. Enunciate and prove the corollaries to this proposition. Trisect a right angle. 3. If a straight line... | |
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