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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. "
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books - Seite 245
von Euclid - 1765 - 464 Seiten
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Science Examination Papers

Great Britain. Education Department. Department of Science and Art - 1899 - 348 Seiten
...AB in D and AC in E, so that DP may be a fourth part of PE. Dl 44. Prove that equal triangles, which have one angle of the one equal to one angle of the other, have the sides about the equal angles reciprocally proportional ; and state and prove the converse...
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Special Reports on Educational Subjects, Bände 6-7

Great Britain. Board of Education - 1900 - 906 Seiten
...inscribed in the smaller circle. 7. Define the terms submultiple, ratio, homologous, duplicate ratio. 8. 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. 4333. M In a given straight...
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Preparatory Schools for Boys: Their Place in English Secondary Education

Great Britain. Board of Education - 1900 - 566 Seiten
...inscribed in the smaller circle. 7. Define the terms submultiple, ratio, homologous, duplicate ratio. 8. 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. In a given straight Hue...
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Examination Papers

University of Toronto - 1900 - 1158 Seiten
...the other, have their sides about the equal angles reciprocally proportional ; and triangles which have one angle of the one equal to one angle of the other and their sides about the equal angles reciprocally proportional are equal to one another. Use this proportion...
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The Contents of the Fifth and Sixth Books of Euclid

Euclid, Micaiah John Muller Hill - 1900 - 190 Seiten
...about the equal angles reciprocally proportional, are equal in area. 49. (i) 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. (ii) Triangles which have one angle...
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The Contents of the Fifth and Sixth Books of Euclid

Micaiah John Muller Hill - 1900 - 165 Seiten
...PROPOSITION XLVIII. (i). (Euc. VI. 14, 1st Part.) ENUNCIATION. Parallelograms having equal areas and having one angle of the one equal to one angle of the other have the sides about the equal angles reciprocally proportional. Let the two parallelograms be placed...
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Selected List of Educational Books for Secondary Schools

Macmillan & Co - 1901 - 776 Seiten
...; .:, by addition, . a + b+e+ ... x+y+z+ ... or a:x 338 EUCLID'S ELEMENTS. PROPOSITION 6. THEOREM. 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. In the A' BAG, EOF, let...
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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - 1901 - 462 Seiten
...vertex of the right 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 third...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

Eldred John Brooksmith - 1901 - 368 Seiten
...diameters. 10. Describe a circle about a given equilateral and equiangular pentagon. 11. Triangles which have one angle of the one equal to one angle of the other and the sides about the equal angles reciprocally proportional, are equal to one another. , Two straight lines...
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Report of the Committee of Council on Education in Scotland...[without Appendix]

1902
...pentagon 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...
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