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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 Elements of Euclid: The Errors by which Theon, Or Others, Have Long ... - Page 141
by Robert Simson - 1827 - 513 pages
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Examinations Papers

1899
...Shew that the area of the hexagon is threefourths that of the regular circumscribed hexagon. 3. If two triangles have one angle of the one equal to one angle...about the equal angles proportionals, the triangles are similar. If the perpendicular from the vertex of a triangle to the base falls within the triangle...
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New Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 382 pages
...86, cor. 5, they can be proved to be mutually equiangular. 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, B, Given A AlBlCl, A2B2C2, such that Z...
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NEW PLANE GEOMETRY

WPPSTER WOODRUFF BEMAN, DAVID EUGENE SMITH - 1899
...sides of the 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 = Z (72...
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Science Examination Papers

Great Britain. Education Department. Department of Science and Art - Examinations - 1899
...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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Proceedings of the Edinburgh Mathematical Society, Volumes 17-18

Edinburgh Mathematical Society - Mathematics - 1899
...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....
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Preparatory Schools for Boys: Their Place in English Secondary Education

Great Britain. Board of Education - Boys - 1900 - 531 pages
...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...equal angles proportionals, the triangles shall be similar. In a given straight Hue PQ a point M is taken and PQ is produced to ‹ so that MO is a mean...
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Special Reports on Educational Subjects, Volumes 6-7

Great Britain. Board of Education - Education - 1900
...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...equal angles proportionals, the triangles shall be similar. 4333. M In a given straight line PQ a point M is taken and PQ is produced to 0 so that MO...
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Sessional Papers, Volume 22, Part 2

Great Britain. Parliament. House of Commons - Great Britain - 1900
...submultiple, ratio, homologous, duplicate ratio. 8. If two triangles have one angle of the one equal to onę angle of the other, and the sides about the equal angles proportionals, the triangles shall lx) similar. In a given straight line PQ a point M is taken and PQ is produced to 0 so that MO is a...
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Examination Papers

University of Toronto - 1900
...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 - Euclid's Elements - 1900 - 143 pages
...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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