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" Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar. "
The Elements of geometry; or, The first six books, with the eleventh and ... - Page 135
by Euclides - 1855
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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...
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Exercises on Euclid and in modern geometry, New ed., revised

James McDowell - 1878 - 312 pages
...DEF are equiangular (constr.), therefore ABC and DEF are also equiangular. QED 81. If two triangles have an angle of the one equal to an angle of the other, and the rectangles under the sides about the equal angles equal, a side of each triangle being taken...
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Elements of Geometry and the First Principles of Modern Geometry

Wm. H. H. Phillips - Geometry - 1878 - 236 pages
...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
...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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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...
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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
...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...
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Elements of Geometry

George Albert Wentworth - 1881 - 266 pages
...Wo'' A'B' ~ We'Hyp. Ax. 1 Since AE = A' B', 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' C' let -. A'B'...
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Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1882 - 512 pages
...same subject. The values attached to the questions differ little from one another. 1. Prove that two triangles, which have an angle of the one equal to an angle of the other, and the sides including the equal angles proportional, are similar. A diagonal of a parallelogram is...
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