 | Elias Loomis - Conic sections - 1877 - 458 pages
...triangles is equal to two right angles (Pr. 27) ; therefore the sum of the angles of all the triangles is equal to twice as many right angles as the polygon has sides. But the same angles are equal to the angles of the polygon, together with the angles at the point F,... | |
 | Edward Olney - Geometry - 1877 - 272 pages
...one re-entrant angle. PROPOSITION XV. 233. TJieorem, — The sum of the interior angles of a polygon is equal to twice as many right angles as the polygon has sides, less four right angles. FIo. 187. DEM. — Let n be the, number of sides of any polygon; then the sum... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...the sum of the angles of all the triangles, that is, the sum of the interior angles of the polygon, is equal to twice as many right angles as the polygon has sides minus two. \ DEFINITIONS. 126.. Every proposition has an hypothesis (19), and a conclusion. Thus in... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...... Th. XXIV. Therefore, if, etc. QUERY. THEOREM XXVI. The sum of the interior angles of a polygon, plus four right angles, is equal to twice as many right angles as the polygon has sides. For, take any polygon, as ABCD E. If from any point within it, as F, lines be drawn to the vertices... | |
 | Edward Olney - Geometry - 1883 - 352 pages
...equal, each to each. PROPOSITION XV. 264. Theorem. — The sum of the interior angles of a polygon is equal to twice as many right angles as the polygon has sides, less four right angles. DEMONSTRATION. Let n be the number of aides of any polygon. We are to prove... | |
 | Mathematical association - 1883 - 86 pages
...complementary. THEOR. 26. All the interior angles of any convex polygon together with four right angles are equal to twice as many right angles as the polygon has sides. THEOR. 27. The exterior angles of any convex polygon made by producing the sides in order are together... | |
 | Mathematical association - 1884 - 146 pages
...any convex polygon : A then shall all the interior angles of ABCDE together with four right angles be equal to twice as many right angles as the polygon has sides. Take any point O within the polygon ABCDE, and join O to each of the angular points of the polygon.... | |
 | Association for the improvement of geometrical teaching - Geometry, Modern - 1884 - 150 pages
...equal to two right angles, /. 2. therefore all the interior and all the exterior angles are together equal to twice as many right angles as the polygon has sides ; but the interior angles and four right angles are together equal to twice as many right angles as... | |
 | 1885 - 608 pages
...straight line. 4. Show that the sum of the interior angles of any rectilineal figure together witli four right angles, is equal to twice as many right angles as the figure has sides. 5. Prove that the opposite sides and angles of a parallelogram are equal to one another,... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...they are similar. For, the corresponding angles in each are equal, because any angle in either polygon is equal to twice as many right angles as the polygon has sides, less four right angles, divided PROPOSITION II. THEOREM. The circumference of a circle may be circumscribed... | |
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Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon... 
