| John Narrien - 1845 - 484 pages
...the angle s' EH is equal to twice the angle AFB or OAF, produce FB to K, and FA to M : then because **the exterior angle of a triangle is equal to the sum of** the interior and opposite angles (Euc. 32. 1.), the angle ABK = BAF + AFB; whence 2 ABK = 2 BAF +2... | |
| Alpheus Crosby - 1847 - 190 pages
...aABC + aACB = AmL? M. .-. ACD 4- ACS xa BAG + ABC -j- ACS ? 20. a. ACD *w BAC + ABC ? XXII. A COR. Any **exterior angle of a triangle is equal to the sum of the two interior opposite angles.** It is of course greater than either singly. Draw CE ]| BA, and prove the same from Theor. V. Join AD... | |
| Alexander Ingram - 1851 - 202 pages
...find the angle ACB. Supposing that APB = P, APC =p; CP = d; AC = C\^ - VP L, and BC = R are known. **Since the exterior angle of a triangle is equal to the sum of the two interior** and opposite angles ; then the angle AJB = P + IBP, and AIB is also equal to C + CAP ; hence P -f IBP... | |
| George Roberts Perkins - 1856 - 460 pages
...angle ACB of the triangle ACB. THEOREM vI. The exterior angle, formed ly producing one of the sides **of a triangle, is equal to the sum of the two interior** and opposite aaigles of the triangle. In the. triangle ABC, if the side AB be produced to D, the exterior... | |
| George Roberts Perkins - 1860 - 472 pages
...angle ACB of the triangle ACB. THEOREM VI. The exterior angle, formed by producing one of the sides **of a triangle, is equal to the sum of the two interior** and opposite angles of the triangle. In the triangle ABC, if the side AB be produced to D, the exterior... | |
| James Pryde - 1867 - 506 pages
...angle of incidence, their complements are also equal ; hence L BAD = L SAF, and L DBC = L GBA. But **since the exterior angle of a triangle is equal to the sum of the two interior** angles, L. EBC = L ВАС + L. ACB = L. BAD + L DAG + L ACB = L. BAD + L SAF + L ACB = 2 L BAD + L... | |
| Richard Wormell - 1868 - 286 pages
...It follows that in a right-angled triangle two angles are acute, and their sum is a rightangle. 127. **The exterior angle of a triangle is equal to the sum of** the interior and opposite angles. F'g- 1°3- When the side of a triangle is produced, the new angle... | |
| Richard Wormell - 1870 - 304 pages
...rightangles, these two straight lines are parallel (§ 100). Consequences of the above properties. 20. **The exterior angle of a triangle is equal to the sum of** the interior and opposite angles ; and the three angles of a triangle are together equal to two right-angles... | |
| Edward Olney - 1872 - 472 pages
...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 of the two interior** non-adjacent angles. DEM. — Let ABC be any triangle, and CBD an exterior angle; then CBD = A + C.... | |
| Edward Olney - 1872 - 562 pages
...by any side with its adjacent side produced, as CBD, Fig. 174. PROPOSITION IT. 231. TJieorem. — An **exterior angle of a triangle is equal to the sum of the two interior** non-adjacent angles. DEM. — Let ABC be any triangle, and CBD an exterior angle; then CBD = A + e.... | |
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