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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 Elements of Euclid, containing the first six books, with a selection of ... - Σελίδα 199
των Euclides - 1874
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Elementary Geometry: Practical and Theoretical

Charles Godfrey, Arthur Warry Siddons - 1903 - 384 σελίδες
...§AB, 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...

The School World: A Monthly Magazine of Educational Work and Progress, Τόμος 5

1903 - 692 σελίδες
...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...

Interim Report of the Commissioners on Certain Parts of Primary Education ...

...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...

Manual

1903 - 896 σελίδες
...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...

A Text-book of Euclid's Elements for the Use of Schools, Βιβλίο 1

Euclid - 1904 - 488 σελίδες
...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...

Calendar of the University of Sydney

University of Sydney - 1904 - 680 σελίδες
...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...

Calendar, for the Year ...

1905 - 212 σελίδες
...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...about the equal angles proportionals, the triangles are similar. '2. ABCD, AEFG are two squares so placed that the angles at A coincide. Show that A, F,...

Science Examinations ... Reports, Etc

1906 - 502 σελίδες
...; 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...

The New International Encyclopaedia, Τόμος 18

Daniel Coit Gilman, Harry Thurston Peck, Frank Moore Colby - 1906 - 936 σελίδες
...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,...

Annual Report of the Commissioners ..., Τόμος 73

1907 - 608 σελίδες
...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...the sides about the equal angles proportionals ; the remaining angles are equal, each to each, viz., those which are opposite to the homologous sides. 5....