The areas of 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. B' ADC A' D' C' Hyp. In triangles ABC and A'B'C', ZA = ZA'. Plane Geometry - Page 180by Arthur Schultze - 1901Full view - About this book
| Euclid - 1859 - 150 pages
...rpiywvwv, àvriirtirèvQaaiv at ir\tvpai, ai irepi ràç; îffaç ywviaç, laa iariv iKtlva. Equal **triangles which have an angle of the one equal to an angle of the other** have their sides about the equal angle* reciprocally proportional ; and triangles which have an angle... | |
| George Roberts Perkins - Geometry - 1860 - 472 pages
...this series of equal ratios (T. VI.) : BC : B'C' : : AC : A'C' : : AB : A'B'. GEOMETRY. THEOREM T1ll. **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. In the two triangles ABC, A'B'C',... | |
| Benjamin Greenleaf - Geometry - 1862 - 532 pages
...properties of triangles include, by implication, those of all figures. PROPOSITION XXIV . — THEOREM. 264. **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... | |
| Benjamin Greenleaf - Geometry - 1862 - 518 pages
...properties of triangles include, by implication, those of all figures. PROPOSITION XXIV. — THEOREM. 264. **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... | |
| Benjamin Greenleaf - Geometry - 1863 - 504 pages
...properties of triangles include, by implication, those of all f1gures. PROPOSITION XXIV. — THEOREM. 264. **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... | |
| Euclides - 1863 - 122 pages
...angles reciprocalla proportional (tbat is, DB is to BE a« GB /stoBF); and, converseln, parallelograms **which have an angle of the one equal to an angle of the other,** and their sides about the equalangles reciprocallg proportional, are equal to one another. Place the... | |
| Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...: hence, it is also similar to DFE. Therefore, two triangles, etc. THEOREM V. Two triangles having **an angle of the one equal to an angle of the other,** and the sides about those angles proportional, are similar. Let the two triangles ABC, DEF, have the... | |
| Euclides - 1865 - 402 pages
...the three sides of a triangle to the opposite angles meet in the same point. 14. If two trapezinms **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... | |
| Benjamin Greenleaf - Geometry - 1868 - 340 pages
...properties of triangles include, by implication, those of all figures. PROPOSITION XXIV. — THEOREM. 264. **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, PEF have... | |
| E. M. Reynolds - Geometry - 1868 - 172 pages
...A'B'C'. Relation of Areas of Figures. THEOREM VI. Triangles which have one angle of the one equal to one **angle of the other, are to each other as the products of the sides** containing the equal angle. Let the triangles ABC, A'BC' have equal angles at B. Then shall ABC : A'BC'... | |
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