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" ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional. "
Junior High School Mathematics ... - Page 66
by Edson Homer Taylor, Fiske Allen - 1923
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Elements of Geometry: Including Plane, Solid, and Spherical Geometry

George Washington Hull - Geometry - 1807 - 408 pages
...triangle, 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 ...

Rev. John Allen - Astronomy - 1822 - 516 pages
...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 - 272 pages
...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 1....
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - Geometry - 1846 - 138 pages
...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 - Geometry - 1854 - 192 pages
...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, if...
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Euclid's Elements of Geometry

Euclid - Geometry - 1872 - 261 pages
...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 1 ....
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 442 pages
...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 * AB AC żA- żA', аж* _=_. We...
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Questions and Exercises on Stewart's Lessons in Elementary Physics

George Anthony Hill - Physics - 1880 - 204 pages
...are 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 triangle...
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Elements of Geometry

George Albert Wentworth - 1881 - 266 pages
...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' A'C' We are to prove А AB С and A'...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...tests of similarity (§ 268) is satisfied. PROPOSITION XX. THEOREM. 275. Two triangles are similar when they have an angle of one equal to an angle of the other, and the sides including these angles proportional. BC In the triangles ABC and A'B'C', let To prove that the...
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