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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 - Σελίδα 170
των Euclid - 1781 - 520 σελίδες
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Elementary Geometry: Practical and Theoretical

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

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

1903 - 692 σελίδες
...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...

Manual

1903 - 898 σελίδες
...right angles to the straight line joining the middle points of AD and BC. 3. Show that if two triangles have one angle of the one equal to one angle of the other, and the sides about another angle of each proportional, the sides opposite the equal angles being homologous,...

Vectors and Rotors: With Applications

Olaus Henrici, George Charles Turner - 1903 - 236 σελίδες
...the theorem is that of Euc. VI. vi., from which the general case follows at once. " 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 similar." For if one triangle...

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

New South Wales. Commission on primary, secondary, technical, and other branches of education - 1903 - 634 σελίδες
...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...

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...

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, for the Year ...

1905 - 214 σελίδες
...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 squares...

Science Examinations ... Reports, Etc

1906 - 502 σελίδες
...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 another,...

The New International Encyclopaedia, Τόμος 18

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