 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 Plane Geometry: For the Use of Schools - Page 71by Nicholas Tillinghast - 1844 - 96 pagesFull view - About this book
 | 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... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 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...proved very briefly in the following manner, if the restriction imposed by Euclid be withdrawn : — Two triangles which have an angle of the one equal to an angle of the other, are to one another in the ratio compounded of the ratios of the sides about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 - 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... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...respects; (i.5) .'. A FGH is equiangular to &ABC, Also, If two A s have one angle of the one equal to one angle of the other, and the sides about the equal angles proportional, then shall the A s be equiangular. B CG ff Let ABC, FGH be two A s, having iBAC=i GFH, and such that... | |
 | 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 : DE... | |
 | 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... | |
 | 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 one equal to... | |
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