| Benjamin Greenleaf - Geometry - 1874 - 206 pages
...the triangle ABC; 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... | |
| L J V. Gerard - 1874
...of homologous 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... | |
| Euclides - 1874 - 234 pages
...sides. Cor. 2. — If the two triangles are equal, ABxAC=POxOQ, therefore ^? - 29 \)L .AO that is, equal **triangles which have an angle of the one equal to an angle of the other,** have the sides ahout the equal angles reciprocally proportional. Cor. 3. — Hence also equiangular... | |
| 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... | |
| 1876 - 646 pages
...polygons. Prove that two triangles are similar when they are mutually equiangular. 2. 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. 3. To inscribe A circle in a given... | |
| Richard Wormell - 1876
...same demonstration it may be shown that THEOREM LXXV. If two parallelograms are equal in area, and **have an angle of the one equal to an angle of the other,** then the sides which contain the angle of the first are the extremes of a proportion of which the sides... | |
| Aaron Schuyler - Geometry - 1876 - 384 pages
...proportionality of sides involve equality of angles. 230. Proposition XXI.— Theorem. Two triangles having **an angle of the one equal to an angle of the other,** and tlie including sides proportional, are similar. In the triangles, ABC, DEF, let A = D, and AB :... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...4 ÊF* = AC1 + SD* + 4 QED GEOMETRY. BOOK IV. PROPOSITION XIII. THEOREM. 341. Two triangles having **an angle of the one equal to an angle of the other are to** each other as the products cf t he sides including the equal angles. Let the triangles ABC and ADE... | |
| Elias Loomis - Geometry - 1877 - 458 pages
...the point D toward B, or from it. D2 PROPOSITION XXI. THEOREM. Two triangles are similar when they **have an angle of the one equal to an angle of the other,** and the sides including those angles proportional. Let the triangles ABC, DEF have the angle A of the... | |
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