 | William Chauvenet - Geometry - 1872 - 382 pages
...other are to each other as the products of the sides including the equal angles. Two triangles which have an angle of the one equal to an angle of the other may be placed with their equal angles in coincidence. Let ABC, ADE, b« the two triangles having the... | |
 | William Frothingham Bradbury - Geometry - 1872 - 124 pages
...DEH are equiangular (I. 35), and similar (20) ; therefore : EF D THEOREM X. 231 Two triangles having an angle of the one equal to an angle of the other, and the sides including these angles proportional, are similar. In the triangles ABC,DEF let tiifl angle... | |
 | William Frothingham Bradbury - Geometry - 1872 - 262 pages
...(I. 35^, and similar (20) ; therefore BG:EH—AB:DE=AC:DF=BC:EF THEOREM X. 23, Two triangles having an angle of the one equal to an angle of the other, and the sides including these angles proportional, are similar. E D In the triangles ABC, DEF let t!:e... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...of the ratio of similitude of the triangles. PROPOSITION VIII.— THEOREM. 22. Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. Two triangles which have... | |
 | Thomas Steadman Aldis - 1872 - 84 pages
...of "proportional compasses." 2. Two triangles have their altitudes proportional to their bases, and an angle of the one equal to an angle of the other, adjacent to the bases; prove that they are similar. 3. Prove that two quadrilateral figures are similar... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...hence the triangles DEF, ABC are also equiangular and similar. THEOREM XV. 208. Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing these angles proportional, are similar. Let the two triangles ABC, DEF have the... | |
 | David Munn - 1873 - 160 pages
...opposite angles 42 VII. To find the area of any polygon 43 EXERCISES (4) 44 VIII. Two triangles which have an angle of the one equal to an angle of the other, are to each other as the products of the sides including the equal angles 47 IX. The areas of similar... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...hence the triangles DEF, ABC are also equiangular and similar. THEOREM XV. 208. Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing these angles proportional, are similar. Let the two triangles ABC, DEF have the... | |
 | Euclides - 1874 - 342 pages
...of the intercepted area, according as they intersect internally or externally. 15. If two trapeziums have an angle of the one equal to an angle of the other, and if, also, the sides of the two figures, about each of their angles, be proportionals, the remaining... | |
 | L J V. Gerard - 1874 - 428 pages
...angles are not reciprocally proportional. THEOREM 18. (Eucl. VI. 16.) Two equivalent triangles which have an angle of the one equal to an angle of the other, have the sides of these angles reciprocally proportional. Let there be two equivalent triangles, ABC... | |
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... have an angle of the one equal to an angle of the other, and the sides about those angles reciprocally proportional, are equal to une another. 
