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" 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 equiangular, and shall have those angles equal which are opposite to the homologous sides. "
Euclid's Elements of Geometry,: From the Latin Translation of Commandine. To ... - Page 163
by Euclid, John Keill - 1733 - 397 pages
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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - Geometry - 1901 - 460 pages
...angle which make equal angles with one of the sides. MISCELLANEOUS EXERCISES 1. If two triangles have one angle of the one equal to one angle of the other, and a second angle of the one supplementary to a second angle of the other, then the sides about the...
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Report of the Committee of Council on Education in Scotland...[without Appendix]

Education - 1902 - 942 pages
...is equal to the sum of a side and a diagonal of the smaller pentagon. 5. 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. 12, ABCD is a trapezium in which AB is parallel to and greater than DC,...
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Examinations Papers

1902 - 762 pages
...parallel to them cuts the other sides proportionally. 4. Triangles which are equal in area, and which have one angle of the one equal to one angle of the other, have the sides about the equal angles reciprocally proportional. The diagonals AC, BD of a quadrilateral...
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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 - 634 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 В is parallel to and greater than DC,...
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Elementary Geometry: Practical and Theoretical

Charles Godfrey, Arthur Warry Siddons - Geometry - 1903 - 384 pages
...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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Manual

1903 - 898 pages
...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,...
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Vectors and Rotors: With Applications

Olaus Henrici, George Charles Turner - Graphic statics - 1903 - 236 pages
...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...
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Calendar of the University of Sydney

University of Sydney - 1904 - 680 pages
...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 piece of metal, whose height is 3 ft., and...
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A Text-book of Euclid's Elements for the Use of Schools, Book 1

Euclid - Euclid's Elements - 1904 - 488 pages
...that the triangle AEF is a mean proportional between the triangles FBD, EDC. 2. If two triangles have one angle of the one equal to one angle of the other, and a second angle of the one supplementary to a second angle of the other, then the sides about the...
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Calendar, for the Year ...

1905 - 212 pages
...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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