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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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Elementary geometry

James Maurice Wilson - 1878
...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
...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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First B.A. Examination, University of London: A Hand-book to the Study of ...

J. G - 1878 - 372 pages
...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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Elements of Geometry and the First Principles of Modern Geometry

Wm. H. H. Phillips - Geometry - 1878 - 236 pages
...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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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...(55), and 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 ...

District of Columbia. Board of Education - Education - 1881 - 314 pages
...analysis. 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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Elements of Geometry

George Albert Wentworth - 1881
...the squares on the diagonals. GEOMETRY. — BOOK IV. PROPOSITION XIII. THEOREM. 3-41. Two triangles having an angle of the one equal to an angle of the other are to each other an the products of the sides including the equal angles. Let the triangles ABC and...
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Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1882 - 512 pages
...ratio of AN to NB is the duplicate of the ratio of AM to MB. 2. If two triangles of equal area have an angle of the one equal to an angle of the other, prove that the sides about the equal angles are reciprocally proportional. 3. Shew how to divide a...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1882 - 292 pages
...(V. 4) similar. Proposition 6. Theorem. — 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 will be similar. Let the triangles ABC, DEF have the angle A equal to the angle D, and...
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Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with ...

Edward Olney - Geometry - 1883 - 354 pages
...Fig. 183. PROPOSITION V. 373. Theorem.— Two triangles having an angle in one equal to an' angle in the other, and the sides about the equal angles proportional, are similar. •' ' > AC DF CB FE' DEMONSTRATION. Let ABC and DEF have the angle* C and F equal, and We are to prove...
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