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 Geometry - Page 65by Adrien Marie Legendre - 1841 - 235 pagesFull view - About this book
| L J V. Gerard - 1874
...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... | |
| 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
...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
...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 - Geometry - 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 to... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...BC* + Vb* + Ш2 = 4 + 4 ^V + 4 4 QED GEOMETRY. BOOK IV. PROPOSITION XIII. THEOREM. 341. 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. Let the triangles ABC and... | |
| 1877
...given equilateral and equiangular pentagon. 9. If two triangles have one angle of the one equal to one **angle of the other, and the sides about the equal angles proportional,** the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous... | |
| George Albert Wentworth - Geometry - 1877 - 398 pages
...Ж? + m? + DA2 = 4 2 + * 2 + 4 4 QED GEOMETRY. BOOK IV. PROPOSITION XIII. THEOREM. 341. Two triangles **having an angle of the one equal to an angle of the** oiher are to each other as the products of the sides including the equal angles. Д Let the triangles... | |
| James McDowell - 1878
...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... | |
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