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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw... Elements of Geometry and Trigonometry - Side 86av Adrien Marie Legendre - 1836 - 359 siderUten tilgangsbegrensning - Om denne boken
| Adrien Marie Legendre - 1841 - 235 sider
...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),... | |
| James Bates Thomson - 1844 - 237 sider
...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... | |
| Nicholas Tillinghast - 1844 - 96 sider
...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 Thomson - 1845 - 358 sider
...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... | |
| 1845
...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
...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 - 1847 - 308 sider
...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 - 1848 - 324 sider
...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 - 1849 - 226 sider
...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... | |
| George Roberts Perkins - 1850 - 320 sider
...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 similar, we... | |
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