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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 of the Elements of Euclid, with numerous exercises - Seite 126
von Euclides - 1853 - 147 Seiten
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Elementary Geometry: Practical and Theoretical

Charles Godfrey, Arthur Warry Siddons - 1903 - 355 Seiten
...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,...
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Calendar

University of Sydney - 1904
...the 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...about the equal angles reciprocally proportional. 8. Find the weight of a conical piece of metal, whose height is 3 ft., and the radius of its base 2...
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A Text-book of Euclid's Elements for the Use of Schools, Bücher 1

Euclid - 1904 - 456 Seiten
...angle of the other, have their sides about the equal angles reciprocally proportional. Conversely, parallelograms which have one angle of the one equal to one angle of the other, and the sides about these angles reciprocally proportional, are equal in area. L GC Let the parm" AB,...
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Calendar, for the Year ...

1905
...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...
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The New International Encyclopaedia, Band 18

Daniel Coit Gilman, Harry Thurston Peck, Frank Moore Colby - 1906
...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...
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Science Examinations ... Reports, Etc

1906
...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...
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Annual Report of the Commissioners ..., Band 73

1907
...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,...
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Calendar

University of Allahabad - 1907
...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...
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Calendar, Teil 1

University of Calcutta - 1907
...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. If a polygon is divided...
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Intermediate Geometry: Being Sections V and VI of "geometry, Theoretical and ...

Walter Percy Workman - 1908
...thenproveT.il andT.llcby means of Ar.6. 309. THEOREM [Ar.7.]. — It two triangles (or two parallelograms) have one angle of the one equal to one angle of the other, their areas are in the ratio of the products of tbe •ides containing the equal angles. (i) In Fig....
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