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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 and the Eleventh and Twelfth Books of Euclid's Elements: With ... - Page 143
by Euclid, James Thomson - 1837 - 390 pages
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The School World: A Monthly Magazine of Educational Work and Progress

Education - 1903
...converse. If two triangles are equiangular their corresponding sides are proportional ; and the converse. 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 internal bisector of an angle of a...
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Elementary Geometry: Practical and Theoretical

Charles Godfrey, Arthur Warry Siddons - Geometry - 1903 - 355 pages
...žAB, OQ = J5 AC ; join PQ ; measure L.' P, Q, and compare them with L.' B, C. =o fig. 313. THEOREM 5. 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. fig. 314. Data ABC, DEF are two triangles...
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Interim Report of the Commissioners on Certain Parts of Primary Education ...

New South Wales. Commission on primary, secondary, technical, and other branches of education - Education - 1903 - 619 pages
...pentagon is equal to the sum of a side and a diagonal of the smaller pentagon. 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. A BCD is a trapezium in which Л...
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Manual

1903
...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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A Text-book of Euclid's Elements for the Use of Schools, Book 1

Euclid - Euclid's Elements - 1904 - 456 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

University of Sydney - 1904
...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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Calendar, for the Year ...

1905
...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...the sides about the equal angles proportionals, the triangles are similar. '2. ABCD, AEFG are two squares so placed that the angles at A coincide. Show...
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Science Examinations ... Reports, Etc

1906
...; 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...and the sides about the equal angles proportionals, show that the triangles are equiangular to one another, and that those angles are equal which are opposite...
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The New International Encyclopaedia, Volume 18

Daniel Coit Gilman, Harry Thurston Peck, Frank Moore Colby - Encyclopedias and dictionaries - 1906
...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 ╗ides proportional, the triangles are similar. If two triangles have their sides proportional,...
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Annual Report of the Commissioners ..., Volume 73

1907
...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...those which are opposite to the homologous sides. 5. Parallelograms upon the same base and between the same parallels are equal to one another. SECTION...
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