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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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C'... "
First Part of an Elementary Treatise on Spherical Trigonometry - Page 69
by Benjamin Peirce - 1836 - 71 pages
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Elements of Geometry, Conic Sections, and Plane Trigonometry

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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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 442 pages
...EH AE = B'C'' A'B' B'C' =A'B', Hyp. Ax. 1 Cons. PROPOSITION VI. THEOREM. 284. Two triangles having an angle of the one equal to an angle of the other, and the including sides proportional, are similar. A A' In. the triangles ABC and A' B' С' let /А / Л1 *...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...4 F* = AC1 + SD* + 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 cf t he sides including the equal angles. Let the triangles ABC and...
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Exercises on Euclid and in Modern Geometry

James McDowell - 1878 - 312 pages
...triangle being taken to 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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Elements of Geometry and the First Principles of Modern Geometry

Wm. H. H. Phillips - Geometry - 1878 - 236 pages
...ABD = ABF " (2, Cor. 3). ABE BE .. . ABC ABD The same is true of parallelograms. BE BF' VI. Theorem. If two triangles have an angle of the one equal to an angle of the other, the ratio of their areas is equal to that of the products of the sides which contain those angles....
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First B.A. Examination, University of London: A Hand-book to the Study of ...

J. G - 1878 - 408 pages
...secant contained between the point and the parallels. 14. // two parallelograms are equal in area, and have an angle of the one equal to an angle of the other, then tfie sides which contain Vie angle of the first are the extremes of a proportion of which the...
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Elementary geometry

James Maurice Wilson - 1878 - 450 pages
...have two adjacent sides of the one respectively equal to two adjacent sides of the other, and likewise an angle of the one equal to an angle of the other ; the parallelograms are identically equal. Part. En. Let A BCD, EFGH be two parallelograms which have...
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

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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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...we have AB:AG — AC:AH But by hypothesis AB : D F.= AC : DF THEOREM XXIV. 60i Two triangles having an angle of the one equal to an angle of the other, and the sides including these angles proportional, are similar. In the triangles ABC, DBF let the angle A = D and...
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Report of the Board of Education to the Commissioners of the District of ...

Education - 1881 - 314 pages
...TENTH GRADE. MAY itf. GEOMETRY AND TRIGONOMETRY. (Twenty credits.) 1. Theorem: — Two triangles having an angle of the one equal to an angle of the other, and the sides including these angles proportional, are similar. 2. If from the diagonal BD of a square ABCD, BE be...
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