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" If two triangles have an angle of one equal to an angle of the other, their areas are to each other as the products of the sides including the equal angles. Given two triangles ABC and A'B'C', having the angle A equal to the angle A'. "
The Elements of Plane Geometry - Side 180
av Charles Austin Hobbs - 1899 - 240 sider
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Elements of Geometry: Including Plane, Solid, and Spherical Geometry

George Washington Hull - 1807 - 398 sider
...they are similar to each other. PROPOSITION XVIII. THEOREM. 254. Two triangles are similar when they have an angle of one equal to an angle of the other, ancL the sides including these angles proportional. *BD* Given — The triangles ABC and DEF, with...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Euclid, Rev. John Allen - 1822 - 494 sider
...HG, and of PB to BL or HE. Cor. 1. — By a similar reasoning it may be proved, that triangles, which have an angle of one, equal to an angle of the other, are to each other, in a ratio, compounded of the ratios, of the sides including the equal angles. Cor....
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Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846
...equal angles are reciprocally proportional (AB to BC as 1.I! to BD. And if two triangles (ABD and CBL), have an angle of one equal to an angle of the other, and the sides about the equal angles reciprocally proportional, they will be equal to one another. PART...
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - 1846 - 138 sider
...opposite sides and angles of a parallelogram are equal : p. 34ofb. 1. 15 Th. Equal triangles which have an angle of one equal to an angle of the other, have their sides about the equal angles reciprocally proportional : and triangles are equal, which...
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Elements of geometry and mensuration

Thomas Lund - 1854 - 192 sider
...that ab : AB :: be : BC ; and by making C the centre, that be : BC :: ac : AC. COR. 1. Conversely, if two triangles have an angle of one equal to an angle of the other, and the sides forming the equal angles proportionals, the triangles will be similar. COR. 2. Hence, also,...
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Euclid's Elements of Geometry

Euclid - 1872 - 261 sider
...equal angles are reciprocally proportional (AB to BC as LB to BD). And if two triangles (ABD and CBL), have an angle of one equal to an angle of the other, and the sides about the equal angles reciprocally proportional, they will be equal to one another. PART...
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Questions and Exercises on Stewart's Lessons in Elementary Physics

George Anthony Hill - 1880 - 188 sider
...equiangular with respect to each other. (b) K they have their homologous sides proportional. (c) If they have an angle of one equal to an angle of the other, and the sides including these angles proportional. (18) The perpendicular upon the hypothenuse of a right...
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College Algebra

Webster Wells - 1890 - 577 sider
...similar, as also are the triangles EOG and COD ; for, by Geometry, two triangles are similar when they have an angle of one equal to an angle of the other, and the including sides proportional. Then the figure OFEG is similar to OBDC, and hence OFEG is a parallelogram....
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Plane and Solid Geometry: Suggestive Method

Charles Ambrose Van Velzer, George Clinton Shutts - 1894 - 395 sider
...the base, PROPOSITION XV. Two triangles which are mutually equiangular are similar. PROPOSITION XVI. If two triangles have an angle of one equal to an angle of the other, and the side* including the equal angles proportional, the triangles are similar. PROPOSITION XVII. Two...
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An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - 1894 - 138 sider
...side and equal to onehalf of it. 4. The two tangents to a circle from an outside point are equal. 5. If two triangles have an angle of one equal to an angle of the other they are to each other as the product of the sides including the equal angles. 6. From the obtuse angle...
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