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" 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 65
by Adrien Marie Legendre - 1841 - 235 pages
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The elements of geometry, in eight books; or, First step in applied logic

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...
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Elements of Geometry with Exercises for Students: An an Introduction to ...

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...
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Report, Volumes 11-20

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...
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Syllabus of Plane Geometry: (corresponding to Euclid, Books I-VI) ...

Association for the improvement of geometrical teaching - Geometry, Plane - 1876 - 58 pages
...two adjoining sides of the one respectively equal to two adjoining sides of the other, and likewise an angle of the one equal to an angle of the other; the parallelograms are identically equal. [By Superposition.] COR. Two rectangles are equal, if two...
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Modern geometry [ed.] with an appendix by W.B. Jack

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...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

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...
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Elements of Plane and Solid Geometry

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...
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Report of Her Majesty's Civil Service Commissioners: Together ..., Volume 21

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...
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Elements of Plane and Solid Geometry

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...
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Exercises on Euclid and in modern geometry, New ed., revised

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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