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" If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides. "
A Shorter Geometry - Page xvi
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Manual

1903 - 896 pages
...that the square on DE is equal to twice the rectangle contained by the radii of the two circles. 4. If two triangles have one angle of the one equal to one an^le of the other, and the sides about the equal angles proportionals, show that the triangles are...
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Calendar of the University of Sydney

University of Sydney - 1904 - 680 pages
...iu-radius and the circum-radius respectively measure 1 ft. and " ft. 1 in. 7. Equal triangles, which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional. 8. Find the weight of a conical...
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A Text-book of Euclid's Elements for the Use of Schools, Book 1

Euclid - Euclid's Elements - 1904 - 488 pages
...first. [Book vi. Def. 4.] PROPOSITION 14. THEOREM. Parallelograms which are equal in area, and which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional. Conversely, parallelograms which...
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Calendar, for the Year ...

1905 - 212 pages
...the tangent. ((/) About a given circle circumscribe a triangle equiangular to a given triangle. (e) If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles are similar. '2. ABCD, AEFG are two squares so placed...
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Science Examinations ... Reports, Etc

1906 - 502 pages
...; Failed, 21 ; Total, 94. The work in this Stage quite reaches the standard of last year. A. Q. 41. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, show that the triangles are equiangular to one another, and that those...
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The New International Encyclopaedia, Volume 18

Daniel Coit Gilman, Harry Thurston Peck, Frank Moore Colby - Encyclopedias and dictionaries - 1906 - 936 pages
...QVIPRILATKRI LS. one respectively parallel or perpendicular to the sides of the other, they are similar. If two triangles have one angle of the one equal to one angle of the other, and the including ģides proportional, the triangles are similar. If two triangles have their sides proportional,...
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Annual Report of the Commissioners ..., Volume 73

1907 - 608 pages
...rectilineal figure which shall be similar to one, and equal to another given rectilineal figure. 4. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals ; the remaining angles are equal, each to each, viz., those which are...
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The New Zealand University Calendar, Volume 35

University of New Zealand - 1907 - 422 pages
...parallel to one side of a triangle, the other sides are divided proportionally; and the converse. It' two triangles have one angle of the one equal to one angle of the other, and the sides about their equal angles proportional, the triangles are similar. The internal bisector of an angle of a...
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Calendar

University of Allahabad - 1908 - 568 pages
...converse. If two triangles are equiangular, their corresponding ģidee are proportional ; and the converse. If two triangles have one angle of the one equal to...angle of the other, and the sides about these equal angleĢ proportional, the triangles are similar. The internal bisector of an angle of a triangle divides...
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Science Examination Papers

Great Britain. Education Department. Department of Science and Art - 1908 - 328 pages
...angles ABC, DEF are equal, and the angles ACB, DFE are supplementary ; show that AB : DE = AC: DF. If two triangles have one angle of the one equal to one angle of the other, and the sides about one other angle in each proportional, so that the sides opposite equal angles correspond, show that...
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