 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 and Solid Geometry - Page 146by George Albert Wentworth - 1877 - 398 pagesFull view - About this book
 | Euclides - 1874 - 342 pages
...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... | |
 | L J V. Gerard - 1874 - 428 pages
...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
...equal PKOP. XI— THEOREM. (Euc. VI. 14, 15.) Equal parallelograms and equal triangles, which have an angle of the one equal to an angle of the other, have their sides about the equal angles reciprocally proportional; and conversely. Let MB and BN be... | |
 | Aaron Schuyler - Geometry - 1876 - 384 pages
...sides, nor does 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
...Define similar 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... | |
 | Richard Wormell - 1876 - 268 pages
...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... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...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... | |
 | James McDowell - 1878 - 310 pages
...form a rectangle, then shall the triangles be equiangular (VI. 5, 16) 54 81. If two triangles have an angle of the one equal to an angle of the other and the rectangle under the sides about the equal angles equal, a side of each triangle being taken to form... | |
 | Āryabhaṭa - 1878 - 100 pages
...equal (E. 1. 8). I PROP. xix. TIIEOIIEM. (E. 6. 14, 15). Equal triangles and parallelograms laving an angle of the one, equal to an angle of the other, have their sides about th« equal angles, reciprocally proportional. And conversely triangles and parallelograms... | |
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