| David Munn - 1873 - 160 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...the products of the sides including the equal angles** 47 IX. The areas of similar triangles are to each other as the squares of their like sides 48 X. The... | |
| 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... | |
| 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... | |
| Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 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... | |
| L J V. Gerard - 1874 - 428 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... | |
| William Chauvenet - Geometry - 1875 - 466 pages
...GEOMETRY.—BOOK IV. THEOREMS. 219. Two triangles which have an angle of the one equal to the supplo mcnt of **an angle of the other are to each other as the products of the** siiitM including the supplementary angles. (IV. 22.) 220. Prove, geometrically, that the square described... | |
| 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...products of the sides including the equal angles.** 3. To inscribe A circle in a given triangle. 4. The side of a regular inscribed hexagon is equal to... | |
| Richard Wormell - 1876 - 268 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... | |
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