| Euclides - 1840 - 82 pages
...other, and the sides about the equal angles reciprocally proportional, are equal. PROP. XV. THEOR. Equal **triangles which have an angle of the one equal to an angle of the other,** have the sides about the equal angles reciprocally proportional : and triangles which have an angle... | |
| Adrien Marie Legendre - Geometry - 1841 - 235 pages
...right-angled triangles. Thus the general properties of triangles involve those of all figures. THEOREM. 208. **Two triangles, which have an angle of the one equal to an angle of the other, and the sides** about these angles proportional, are similar. fig. 122. Demonstration. Let the angle A = D (fig. 122),... | |
| Nicholas Tillinghast - Geometry, Plane - 1844 - 96 pages
...equiangular with ABC ; and therefore (by the Corollary to the last Proposition) similar. PROP. XVII. **THEOREM. Two triangles, which have an angle of the one equal to an angle of the other, and the sides** about the equal angles proportional, are similar. In the triangles ABC, DEF, let the angles, C, F,be... | |
| James Bates Thomson - Geometry - 1844 - 237 pages
...triangle AGH is similar to ABC ; therefore DEF is also similar to ABC. Hence, If any two triangles **have an angle of the one equal to an angle of the...and the sides containing those angles proportional,** those two triangles are similar. PROPOSITION XXI. THEOREM. Two triangles, ABC, DEF, which have their... | |
| Euclid, James Thomson - Geometry - 1845 - 380 pages
...AB is equal to the parallelogram BC. Therefore equal parallelograms, &c. PROP. XV. THEOR. — Equal **triangles which have an angle of the one equal to an angle of the other,** have their sides about those angles reciprocally proportional : and (2) triangles which have an angle... | |
| Nathan Scholfield - 1845 - 896 pages
...properties of triangles include, by implication, those of all figures. FROPOSITION XIX. THEOREM.Two **triangles, which have an angle of the one equal to an angle of** tlie other, and the sides containing those angles proportional, are similar, In the two triangles ABC,... | |
| Euclides - 1846 - 272 pages
...right, since they are equal to these right angles (by Prop. 34.) CoR. 2. — If two parallelograms **have an angle of the one equal to an angle of the other,** the remaining angles will be also equal ; for the angles which are opposite to these equal angles are... | |
| George Roberts Perkins - Geometry - 1847 - 308 pages
...must also be proportional to the sides GH, HK ,( B. IV, Def. 3). 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 similar,... | |
| George Clinton Whitlock - Mathematics - 1848 - 324 pages
...Trapezoid— -consequences, measures, parallelogram, triangle, comparisons, equalities 92 3. Triangles having **an angle of the one equal to an angle of the other** — consequence • 93 4. Exercises.... 94 BOOK THIRD. PLANE GEOMETRY DEPENDING ON THE CIRCLE, ELLIPSE,... | |
| 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...and the sides containing those angles proportional.** Let the triangles ABC, DEF have the angle A of the one, equal to the angle D of the other, and let... | |
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