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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 161
by John Keill - 1733 - 397 pages
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New Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 382 pages
...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...
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NEW PLANE GEOMETRY

WPPSTER WOODRUFF BEMAN, DAVID EUGENE SMITH - 1899
...other, they are similar. PLANE GEOMETRY. [BK. IV. 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. Given AA^Ci, A2B2C2, such that Z Cl...
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The Contents of the Fifth and Sixth Books of Euclid

Euclid, Micaiah John Muller Hill - Euclid's Elements - 1900 - 143 pages
...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 so...
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THE CONTENTS OF THE FIFTH AND SIXTH BOOKS OF EUCLID

M. J. M. HILL - 1900
...angle of the other have the sides about the equal angles reciprocally proportional. (ii) Parallelograms having one angle of the one equal to one angle of the other, and the sides about the equal angles reciprocally proportional, are equal in area. 49. (i) Equal triangles...
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Preparatory Schools for Boys: Their Place in English Secondary Education

Great Britain. Board of Education - Boys - 1900 - 531 pages
...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...
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Examination Papers

University of Toronto - 1900
...to ensure the similarity of two rectilinear figures. Is there any exception t 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 shall be similar. 4. Shew how to...
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Examination Papers

University of Toronto - 1901
...same altitude are to one another as their bases. (Eue. VI, 1.) 7. Equal parallelograms, which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional. (Eue. VI, 14.) 8. APB is any chord of a given circle, drawn through the...
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Selected List of Educational Books for Secondary Schools

Macmillan & Co - Textbooks - 1901 - 776 pages
...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,...
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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - Geometry - 1901 - 440 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
...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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