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. B' ADC A' D' C' Hyp. In triangles ABC and A'B'C', ZA = ZA'. Plane Geometry - Page 180by Arthur Schultze - 1901Full view - About this book
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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 :... | |
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