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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.
Questions and Exercises on Stewart's Lessons in Elementary Physics - Página 178
de George Anthony Hill - 1880 - 188 páginas
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## Elements of geometry: including plane, solid and spherical geometry

George Washington Hull - 1807 - 398 páginas
...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 - 1822 - 494 páginas
...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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## Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - 1829 - 129 páginas
...space of a quadrant, the sides will become parallel each to each. 3. — When they have an angle of the one equal to an angle of the other, and the sides including these angles proportional — . Thus if the F45 angle A=A (fig. 45), and if AB : AD : : AC : AF, then we say the triangles are...
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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 1. — Let...
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## Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - 1846 - 138 páginas
...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 - 362 páginas
...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 a triangle...
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## Catalogue of the Officers and Students

...diagonals of the given quadrilateral. G. 4. Two triangles are similar, if they have an angle of the one equal to an angle of the other and the sides including those angles proportional. 5. In any triangle, if a straight line is drawn from the vertex to the middle...
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## A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1871 - 368 páginas
...proportional. PROPOSITION VI.— THEOREM. 32. Two triangles are similar, when an angle of the one is equal to an angle of the other, and the sides including these angles are proporportional. In the triangles ABC, A'B'C', let A A> A = A', and AB AC A'B' A'C'' / '" s then,...
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## An Elementary Geometry

William Frothingham Bradbury - 1872 - 110 páginas
...equiangular (I. 35), and similar (20) ; therefore : EF D THEOREM X. 231 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,DEF let tiifl angle A =: D and AB : DE= AC : DF then the triangles...
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## Euclid's Elements of Geometry

Euclid - 1872 - 261 páginas
...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 . — Let...
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