| Edward Olney - Geometry - 1872 - 562 pages
...formed 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;... | |
| 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 of the two interior non-adjacent angles. DEM. — Let ABC be any triangle, and CBD an exterior angle;... | |
| 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... | |
| Alfred Hix Welsh - Geometry - 1883 - 326 pages
...degrees in each of the others, and what is the kind of triangle ? 4. Prove that the exterior angle, BCE, of a triangle is equal to the sum of the opposite interior angles a and b. 5. If the opposite interior angles of a triangle are 35° 25', 68° 35', what is the exterior... | |
| John Trowbridge - Physics - 1884 - 408 pages
...obtained very simply by geometry. The propositions necessary to prove it are the following: 1. The exterior angle of a triangle is equal to the sum of the opposite interior angles. 2. Two angles are equal when their sides are mutually perpendicular. 3. The sine of an acute angle... | |
| 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
...half 2^ at center standing on (arc BC + arc DA). PROOF. Join CD. £ BFC = £ BDC + £ DCA. (173. The exterior angle of a triangle is equal to the sum of the opposite interior angles.) But 2 4 BDC = £ at center on BC, and 2 £ DCA = £ at center on DA ; (375. An angle at the center... | |
| George Bruce Halsted - Geometry - 1886 - 394 pages
...= half 4 at center standing on (arc BC + arc DA). PROOF. Join CD. 4 BFC = 4 BDC + 4 DCA. (173. The exterior angle of a triangle is equal to the sum of the opposite interior angles.) But 2 4 BDC = 4 at center on BC, and 2 4 DCA = 4 at center on DA ; (375- An angle at the center is... | |
| Samuel Edward Warren - Geometrical drawing - 1887 - 200 pages
...Fig. 52, are exterior angles. The last theorem now naturally leads to the following : — Theorem. — An exterior angle of a triangle is equal to the sum of the two opposite interior angles. The angles d and CAB, Fig. 53, arc together equal to two right angles,... | |
| George Albert Wentworth - 1889 - 276 pages
...Corollary II. The sum of the acute angles of a right triangle is equal to 90°. y i /" / 32. Theorem. An exterior angle of a triangle is equal to the sum of the two opposite interior angles. X 33. Theorem. The sum of the angles of a quadrilateral is equal... | |
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