 Corresponding Angles and Sides. If two triangles have the angles of the one respectively equal to the angles of the other, the equal angles are called corresponding angles, and the sides opposite these angles are called corresponding sides.  Technical Manual - Σελίδα 90των United States. War DepartmentΠλήρης προβολή - Σχετικά με αυτό το βιβλίο
 | James Mitchell - 1823 - 666 σελίδες
...n - from each oilier only in quantity or magnitude. SIMILAR Plane Figures, in Geometry, are such as have the angles of the one respectively equal to the angles of the other, and the sides about those angles proportional ; and such figures are to each other as the squares of... | |
 | John Radford Young - 1827 - 228 σελίδες
...these angles are therefore equal, and consequently AD bisects the angle BAG. PROPOSITION IX. THEOREM. If two triangles have the angles of the one respectively equal to those of the other, the sides containing the equal angles are proportional. Let the triangles ABC,... | |
 | Nicholas Tillinghast - 1844 - 110 σελίδες
...: 7 : 14, then will 8 : 24 : : 42 : 126. BOOK V. DEFINITIONS. 1 . Similar figures are those, which have the angles of the one respectively equal to the angles of the other, and the sides containing the equal angles proportional. 2. The homologous sides of similar figures... | |
 | Nicholas Tillinghast - 1844 - 108 σελίδες
...equal, it follows that AB : BC : : 06 : be ; and so for all the sides ; hence these polygons, having the angles of the one respectively equal to the angles of the other, and the sides including the equal angles proportional, are similar (B. VI. Def. 1). PROP. II. THEOREM.... | |
 | James Elliot - 1851 - 152 σελίδες
...triangle equal to the fourth part of it. PROPOSITION LXVIII. THEOREM. If two Triangles (ABC and abc) have the Angles of the one respectively equal to the Angles of the other, the Triangles are similar, and the Sides about the equal Angles are proportional. That is, AB : db :: AC... | |
 | George Roberts Perkins - 1856 - 460 σελίδες
...O'=0. We see that the equal angles are opposite the homologous sides. THEOREM vI. Two triangles, which have the angles of the one respectively equal to the angles of the other, are similar, and the sides opposite the equal angles are homologous. In the two triangles ABC, A'B'C',... | |
 | George Roberts Perkins - 1860 - 472 σελίδες
...C'=C. We see that the equal angles are opposite the homologous sides. fHEOREM V1. Two triangles, which have the angl-es of the one respectively equal to the angles of the other, are similar, and the sides opposite the equal angles are homologous. In the two triangles ABC, A'B'C',... | |
 | Richard Wormell - 1871 - 288 σελίδες
...reflection RMN = o MN, therefore, also, i = o, and the triangles MOC, M io, having a common side and the angles of the one respectively equal to the angles of the other, are equal ; consequently oo = i c. Thus the ray MR proceeds as if it came from a point i at the back... | |
 | Edward Olney - 1872 - 270 σελίδες
...two spherical triangles having the sides of the one respectively equal to the sides of the other, or the angles of the one respectively equal to the angles of the other, are equal, or symmetrical and equivalent. DEM.—The sides of the triangles being equal, the facial... | |
 | Edward Olney - 1872 - 472 σελίδες
...two spherical triangles having ihe sides of the one respectively equal to the sides of the other, or the angles of the one respectively equal to the angles of the other, are equal, or symmetrical and equivalent. DEM. — The sides of the triangles being equal, the facial... | |
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