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
| Elias Loomis - Conic sections - 1849 - 252 pages
...similar. Wherefore, two triangles, &c. PROPOSITION XX. THEOREM. Two triangles are similar, when they **have an angle of the one equal to an angle of the other,** and the sides containing those angles proportional. Let the triangles ABC, DEF have the angle A of... | |
| George Roberts Perkins - Geometry - 1850 - 332 pages
...also be proportional to the sides GH, HK, (B. IV, Def. III.) Therefore, the two triangles ABC, GHK **have an angle of the one equal to an angle of the other,** and the sides about those angles proportional, and consequently these triangles are similar; and being... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...properties of triangles include, by implication, those of all figures. B 109 D DF., PROPOSITION XX. THEOEEM. **Two triangles, which have an angle of the one equal to an angle of the other,** and the sides containing those angles proportional, are similar. Let ABC, DEF, be two triangles, having... | |
| Euclid - Geometry - 1853 - 176 pages
...(a) Hypoth. (41 I.29. (c) I. 26. fa) I. 29. (6) Hypoth. (c) I. 34. COROLLARY 2. If two parallelograms **have an angle of the one equal to an angle of the other,** the remaining angles shall be respectively equal. For the angles opposite the equal angles are equal... | |
| Charles Davies - Geometry - 1854 - 436 pages
...of triangles include, by implication, those of all f1gures. BOOK IY. 109 D PROPOSITION XX. THEOREM. **Two triangles, which have an angle of the one equal to an angle of the other,** and the sides containing those angles proportional, are similar. Let ABC, DEF, be two triangles, having... | |
| William Somerville Orr - Science - 1854 - 534 pages
...equal to au angle of the other, have their sides about the equal angles reciprocally proportional ; and **triangles which have an angle of the one equal to an angle of the other,** and their sides about those angles reciprocally proportional, are equal to one another. Let the triangles... | |
| Euclides - 1855 - 270 pages
...and hare their sides reciprocally proportional, they are equiangular. PROP. XV. ТНЕORЕМ. Equal **triangles which have an angle of the one equal to an angle of the other,** have their sides about the equal angles reciprocally proportional; and conversely, triangles which... | |
| Euclides - 1855 - 230 pages
...BC the segments of the base (c). PROPOSITION XIV. THEOREM [1.]—If equal parallelograms (AB and BC) **have an angle of the one equal to an angle of the other,** their sides about the equal angles are reciprocally proportional (DB is to BE, as GB is to BF). [3.]... | |
| George Roberts Perkins - Geometry - 1856 - 460 pages
...this series of equal ratios (T. VI.) : BC : B'C' : : AC : A'C' : : AB : A'B'. GEOMETRY. THEOREM vIII. **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',... | |
| Peter Nicholson - Cabinetwork - 1856 - 518 pages
...triangle ABC ; therefore, also, the triangles DEF, ABC, are equiangular and similar. § THEOREM 51. 122. **Two triangles which have an angle of the one equal to an angle of the other,** and the sides about them proportionals, are similar. Let the angle A equal D, and suppose that AB :... | |
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