| Thomas Steadman Aldis - 1872 - 80 pages
...of "proportional compasses." 2. Two triangles have their altitudes proportional to their bases, and **an angle of the one equal to an angle of the other,** adjacent to the bases; prove that they are similar. 3. Prove that two quadrilateral figures are similar... | |
| William Chauvenet - Geometry - 1872 - 382 pages
...of the ratio of similitude of the triangles. PROPOSITION VIII.— THEOREM. 22. 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. Two triangles which have... | |
| Benjamin Greenleaf - Geometry - 1873 - 202 pages
...with 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 the angle A equal to the... | |
| David Munn - 1873 - 156 pages
...perpendiculars on it from the opposite angles 42 VII. To find the area of any polygon 43 EXERCISES (4) 44 VIII. **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 47 IX. The areas of similar... | |
| Benjamin Greenleaf - Geometry - 1874 - 206 pages
...with 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 the angle A equal to the... | |
| Euclides - 1874 - 234 pages
...proved very briefly in the following manner, if the restriction imposed by Euclid be withdrawn : — **Two triangles which have an angle of the one equal to an angle of the other,** are to one another in the ratio compounded of the ratios of the sides about the equal angles. Let ABC... | |
| L J V. Gerard - 1874 - 424 pages
...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 - 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... | |
| Richard Wormell - 1876 - 264 pages
...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 : DE... | |
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