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" ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional. "
An Examination Manual in Plane Geometry - Página 116
por George Albert Wentworth, George Anthony Hill - 1894 - 138 páginas
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School Science and Mathematics, Volumen22

1922 - 948 páginas
...of the circle to A and C; draw OD J.AC; since <B = <AOD, \ve may apply to AsABC and AOD the theorem: If two triangles have an angle of one equal to an angle of the other, the ratio of their areas equals the ratio of the products of the sides including this angle. Hence...
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Catalogue ...

Yale University. Sheffield Scientific School - 1905 - 1074 páginas
...similar triangle is 1o in. What is the area of the second triangle? 6. The areas of two triangles which have an angle of one equal to an angle of the other are to each other as the products of the sides including the equal angles. 7. When is a circle said...
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Plane Geometry

Edward Rutledge Robbins - 1906 - 268 páginas
...common to both ; Z AMN — ZB ; Z ANM = ZC (?) (98). .-. A are similar (?) (313). QED B C 317. THEOREM. If two triangles have an angle of one equal to an angle of the other and the sides including these angles proportional, the triangles are similar. BCE r Given : A ABC and...
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Bulletin, Tema 3

Association of Teachers of Mathematics in the Middle States and Maryland - 1906 - 58 páginas
...straight angle. (Necessary to prove propositions concerning concurrent lines.) *P16. Triangles that have an angle of one equal to an angle of the other, are to each other as the products of the sides containing those angles. *P18. In any obtuse triangle,...
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Exercises in Concrete Geometry: With Supplementary Discussions

David Sands Wright - 1906 - 104 páginas
...similar if — 1. They are mutually equiangular. 2. Their homologous sides are proportional. 3. They have an angle of one equal to an angle of the other, and the sides including the equal angles are proportional. 4. The homologous sides are parallel. 5....
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Plane and Solid Geometry

Edward Rutledge Robbins - 1907 - 428 páginas
...common to both ; Z AMN = ZB; Z ANM = ZC (?) (98). ... A are similar (?) (313). QED B C 317. THEOREM. If two triangles have an angle of one equal to an angle of the other and the sides including these angles proportional, the triangles are similar. D BCE Given : A ABC and...
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Public Documents of Massachusetts, Volumen9

Massachusetts - 1907 - 1342 páginas
...difference of the intersected arcs. 3. Two triangles, having an angle of one equal to an angle of the other, are to each other as the product of the sides including the equal angles. Prove. 4. If the radius of a circle is 3v% what is the area of a sector whose central angle is 152°...
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Plane and Solid Geometry

Edward Rutledge Robbins - 1907 - 428 páginas
...parallel to the other side, the parallelogram formed is equivalent to the trapezoid. 34. If two equivalent triangles have an angle of one equal to an angle of the other, the sides including these angles are reciprocally proportional. 35. The sum of the three perpendiculars...
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New Plane Geometry

Webster Wells - 1908 - 208 páginas
...of the tests of similarity is satisfied. PROP. XV. THEOREM 242. Two triangles are similar when they have an angle of one equal to an angle of the other, and the sides including these angles proportional. Draw A ABC and A'B'C' having ZA = ZA', and the sides...
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First Course in Algebra: With Eight Thousand Examples Including Three ...

Albert Harry Wheeler - 1908 - 700 páginas
...taken parallel to the axis of Y, and accordingly the triangles OfiA and OH' A' are similar, since they have an angle of one equal to an angle of the other, and the included sides proportional. It follows that either of the points A or A' lies on the straight...
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