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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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THE ELEMENTS OF GEOMETRY.

GEORGE BRUCE HALSTED - 1885
...equal.) therefore, by 491, GH = BH'. In the same way HF = H'F', THEOREM VII. 511. Two triangles having one angle of the one equal to one angle of the other, and the sides about these angles proportional, are similar. HYPOTHESIS. B = G, and AB : BC : : FG : GH. CONCLUSION. A ABC...
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Cambridge University Examination Papers.Michaelmas Term,1884 to Easter Term ...

Cambridge University Examination Papers.Michaelmas Term,1884 to Easter Term,1885.Volume XIV - 1885
...shall have those angles equal which are opposite to the homologous sides. 8. Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional. (b) 9. Explain the terms adjacent,...
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Examinations Papers

1886
...two given circles. How many common tangents can be drawn to two circles which cut one another ? 4. If two triangles have one angle of the one equal to one angle of the other and the sides about these angles proportional, they are similar, and those angles which are opposite to the homologous sides...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1886 - 366 pages
...equal.) therefore, by 491, GH = BH'. In the same way HF = H'F', THEOREM VII. 511. Two triangles having one angle of the one equal to one angle of the other, and the sides about these angles proportional, are similar. HYPOTHESIS. B = $. G, and AB : BC : : FG : GH. CONCLUSION. A AB...
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Annual Report

Canada. Department of the Interior - 1888
...figures. 13. Triangles and parallelograms having equal bases are to one another as their altitudes. 14. If two triangles have one angle of the one equal to one angle of tho other, the triangles are to each other in the ratio of the rectangles under the sides containing...
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The Elements of Plane Geometry:pPart I(corresponding to Euclid Books I.-II ...

Association for the Improvement of Geometrical Teaching - Euclid's Elements - 1888
...GH. Therefore AB : CD : : EF : GH. IV. 14, Part ii. QED THEOR. 14. If two triangles or parallelograms have one angle of the one equal to one angle of the other, their areas have to one another the ratio compounded of the ratios of the including sides of the first...
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Examinations Papers

1889
...respectively equal they are similar, and those sides which are opposite to the equal angles are homologous. If two triangles have one angle of the one equal to one angle of the other, and a second angle of the one supplementary to a second angle of the other, then the sides about the third...
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Annual Report of the Schools of New Brunswick

New Brunswick. Board of Education - Education - 1889
...and those which are opposite to the equal angles are homologous sides. 6. Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional. N. В.- --Female candidates will...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - Mathematics - 1889
...are the middle points ofAB, CD, prove that PQ_ is parallel to AC and BD. 10. 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 ; and, conversely, triangles which...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 pages
...the rectangle contained by the sides about the other, the triangles are equal. (ii.) Conversely: — If two triangles have one angle of the one equal to one angle of the other, the rectangle contained by the sides about one of those angles is equal to the rectangle contained...
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