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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: Viz. the First Six Books, Together with the Eleventh ... - Page 149
by Euclides - 1816 - 528 pages
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Calendar, for the Year ...

1895
...Being given a side of a regular pentagon, construct it. 4. Triangles which are equal in area, and which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional. Describe an isosceles triangle equal...
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Calendar, for the Year ...

1897
...cn the same arc. Deduce that all angles in the same segment of a circle are equal to one another. 4. If two triangles have one angle of the one equal to one angle of tt;e oiher, and the sides about the equal angles proportionals, shew that the triangles are similar....
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Examinations Papers

1899
...circle. 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...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
...parallel or 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 Z...
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NEW PLANE GEOMETRY

WPPSTER WOODRUFF BEMAN, DAVID EUGENE SMITH - 1899
...the 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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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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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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Preparatory Schools for Boys: Their Place in English Secondary Education

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