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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. "
The Elements of Geometry - Page 135
by Webster Wells - 1894 - 378 pages
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Elements of Geometry: Including Plane, Solid, and Spherical Geometry

George Washington Hull - Geometry - 1807 - 408 pages
...triangles are similar to a third 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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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 138 pages
...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 - 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. — Let...
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - Geometry - 1846 - 166 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 - 522 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 a triangle...
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Catalogue of the Officers and Students

Trinity College (Hartford, Conn.) - 1870 - 1008 pages
...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 - Geometry - 1871 - 380 pages
...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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Euclid's Elements of Geometry

Euclid - Geometry - 1872 - 284 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 . — Let...
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1872 - 262 pages
...similar (20) ; therefore BG:EH—AB:DE=AC:DF=BC:EF THEOREM X. 23, Two triangles having an angle of the one equal to an angle of the other, and the sides including these angles proportional, are similar. E D In the triangles ABC, DEF let t!:e angle A = D and AB :DE=AC :DF then the triangles...
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