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" Assuming that 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... "
SYLLABUS OF PLANE GEOMETRY - Side 17
1876
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Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 398 sider
...4 ÊF* = 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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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1877 - 443 sider
...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...
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Elementary geometry

James Maurice Wilson - 1878
...THEOREM 29. If two parallelograms have two adjacent sides of the one respectively equal to two adjacent sides of the other, and likewise an angle of the one...other ; the parallelograms are identically equal. Part. En. Let A BCD, EFGH be two parallelograms which have two adjoining sides AB, BC of the one equal...
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Elements of Geometry and the First Principles of Modern Geometry

Wm. H. H. Phillips - 1878 - 209 sider
...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. ELEMENTS...
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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...
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First B.A. Examination, University of London: A Hand-book to the Study of ...

J. G - 1878 - 372 sider
...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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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 - 1880 - 240 sider
...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 - 1881
...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
...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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