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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
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο

New Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - 1899 - 400 σελίδες
...perpendicular to the sides of the other, they are similar. PROPOSITION XVIII. 264. Theorem. If two triangles have one angle of the one equal to one angle of the other, and the including sides proportional, the triangles are similar. A, Bi Given A AiBiCi, A^B2C^, such that...

Science Examination Papers

Great Britain. Education Department. Department of Science and Art - 1899 - 348 σελίδες
...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...

Proceedings of the Edinburgh Mathematical Society

Edinburgh Mathematical Society - 1899 - 344 σελίδες
...joined, the triangles EAB, DAC are halves of the parallelograms BE, CD. Hence, Two triangles which have one angle of the one equal to one angle of the other have to each other the same ratio as the rectangles contained by the sides about the equal angles....

Examination Papers

University of Toronto - 1900 - 1158 σελίδες
...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...

Preparatory Schools for Boys: Their Place in English Secondary Education

Great Britain. Board of Education - 1900 - 568 σελίδες
...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...

The Contents of the Fifth and Sixth Books of Euclid

Euclid, Micaiah John Muller Hill - 1900 - 190 σελίδες
...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...

The Contents of the Fifth and Sixth Books of Euclid

Euclid, Micaiah John Muller Hill - 1900 - 165 σελίδες
...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...

Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - 1901 - 460 σελίδες
...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...

Selected List of Educational Books for Secondary Schools

Macmillan & Co - 1901 - 804 σελίδες
...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,...

Report of the Committee of Council on Education in Scotland...[without Appendix]

1902 - 942 σελίδες
...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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