An exterior angle of a triangle is equal to the sum of the two opposite interior angles, and therefore greater than either of them. Plane Geometry - Page 33by George Albert Wentworth - 1899 - 256 pagesFull view - About this book
| Anna Cabot Lowell - Geometry - 1846 - 206 pages
...other. 134. The exterior angle of a triangle, that is, the angve made by producing one of the sides **of a triangle, is equal to the sum of the two opposite interior angles,** (fig. 88.) Angle ACD = angle ABC + angle CAB. Dem. ACD + ACB = 2 RA; ABC + CAB -f ACB = 2 RA; therefore... | |
| George Clinton Whitlock - Mathematics - 1848 - 338 pages
...Triangle is equal to a right angle Cor. 8. The external angle formed by producing one of (94) the sides **of a triangle, is equal to the sum of the two opposite** internal angles. Let a, b, c, be the three angles of any triangle, and с adjacent to the external... | |
| Michigan. Department of Public Instruction - Education - 1893 - 518 pages
...done in the simplest manner you can conceive. GEOMETRY. Demonstrate the following propositions: 1. Any **exterior angle of a triangle is equal to the sum of the two opposite interior angles.** 2. If the squares of the sides of a quadrilateral are together equivalent to the squares of the diagonals,... | |
| Chicago (Ill.). Board of Education - Elementary schools - 1872 - 130 pages
...right angles. a=db=ec=c d-{-e+c=a + b + c, or a flat angle, or two right angles. THEOREM II.—The **exterior angle of a triangle is equal to the sum of the two opposite interior angles.** g + d= 2 right angles. c+d+e=^2 right angles. g+d=c+d+c. In the following figures, mark and name angles.... | |
| 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;... | |
| 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;... | |
| 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... | |
| George Albert Wentworth - Geometry - 1877 - 436 pages
...one third of two right angles, or two thirds of one right angle. PROPOSITION XXII. THEOREM. 105. The **exterior angle of a triangle is equal to the sum of the two opposite interior angles.** a Let BC H be an exterior angle of the triangle ABC. We are to prove Z BCH= Z. A + ZB Z. B С 11+ Z... | |
| George Anthony Hill - Geometry - 1880 - 348 pages
...53) ? Therefore, m = a -\- c (Axiom I.). That is, — Theorem. — An exterior angle of Fiff- **• **a triangle is equal to the sum of the two opposite interior angles.** Exercises.- — 1. Find the exterior angle of a triangle if the opposite interior angles are 38° 35'... | |
| George Albert Wentworth - 1881 - 266 pages
...one third of two right angles, or two thirds of one right angle. PROPOSITION XXII. THEOREM. 105. The **exterior angle of a triangle is equal to the sum of the two opposite interior angles.** л— — Let BC H be an exterior angle of the triangle ABC. We are to prove ZB СH = ZA + Z B. ZB... | |
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