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" If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar. "
The First Six Books: Together with the Eleventh and Twelfth - Page 170
by Euclid - 1781 - 520 pages
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Woolwich mathematical papers [aftwerw.] Mathematical papers for admission ...

Woolwich roy. military acad - 1884
...in E, shew that AB touches the circumscribing circle of the triangle CDE. 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 triangles which have one angle...
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Examinations Papers

1884
...a given circle. Inscribe a regular figure of ten sides in a given circle. 3. 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. If one of the said sides in the...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884
...= ir BC: ir FE; • ||m AB : ||m FE = ir BC: r FE; PROPOSITION 15. THEOREMS. 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. Conversely : Triangles which have...
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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...
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Key to the Elements of Euclid

John Sturgeon Mackay - Geometry - 1885 - 300 pages
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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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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...
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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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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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