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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 of the Elements of Euclid, with numerous exercises - Seite 126
von Euclides - 1853 - 147 Seiten
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Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1894
...than eight question*. The values attached to the questions are shown in brackets. 1. If two triangles have one angle of the one equal to one angle of the other, and the sides about these equal angles proportional, show that the triangles are similar, and that...
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Calendar, for the Year ...

1895
...circle. 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...about the equal angles reciprocally proportional. Describe an isosceles triangle equal in area to a given triangle and having an angle equal to one of...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - 1895 - 320 Seiten
...parallel or perpendicular to the sides of the other, they are similar. (Why ?) Theorem 9. 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 A A1 B1d, A2B2C2, such that...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - 1895 - 320 Seiten
...parallel or perpendicular to the sides of the other, they are similar. (Why ?) Theorem 9. 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^d, A2B2C2, such that ZG!...
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Science Examination Papers

Great Britain. Education Department. Department of Science and Art - 1899
...meeting 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 of this...
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Proceedings of the Edinburgh Mathematical Society, Bände 17-18

Edinburgh Mathematical Society - 1899
...CD be 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. LIST...
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New Plane Geometry

Wooster Woodruff Beman, David Eugene Smith - 1899 - 252 Seiten
...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. C, Given A A1B^i, AJB^C2, such that...
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New Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - 1899 - 382 Seiten
...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...
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The Contents of the Fifth and Sixth Books of Euclid

Euclid, Micaiah John Muller Hill - 1900 - 143 Seiten
...sides 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...about the equal angles reciprocally proportional. (ii) Triangles which have one angle in the one equal to one angle in the other and the sides about...
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Examination Papers

University of Toronto - 1900
...angle of 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...
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