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" 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 ; and parallelograms that have one angle of the one equal to one angle of the other, and their sides... "
Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... - Page 94
by Dennis M'Curdy - 1846 - 138 pages
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The Elements of Geometry

Henry W. Keigwin - Geometry - 1897 - 250 pages
....'. a : x : : b : y : : c : z. .'. the triangles 1 and 2 are similar. 240. COR. 1. 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. 241. COR. 2. If two triangles...
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Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...an acute angle of one equal to an acute angle of the other. 2. 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. 3. Two triangles are similar when the sides of one...
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The Essentials of Geometry (plane)

Webster Wells - Geometry - 1898 - 284 pages
...the tests of similarity is satisfied. PROP. XVII. THEOREM. 261. 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. B -- fc Given, in &ABC and A' BC', To Prove A ABC...
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Plane and Solid Geometry

William James Milne - Geometry - 1899 - 398 pages
...to their altitudes. 336 c. To the products of their bases by their altitudes. 336 d. If they have an angle of one equal to an angle of the other, to the products of the sides including the equal angles. 340 e. If they are similar triangles, to...
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The Elements of Plane Geometry

Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...each other as the products of the sides including the supplementary angles. Ex. 540. If two triangles have an angle of one equal to an angle of the other, and a second angle of one supplementary to a second angle of the other, the sides about the third angles...
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Syllabus of Propositions in Geometry: Intended for Use in Preparing Students ...

Harvard University - Geometry - 1899 - 39 pages
...respectively equal to two angles of the other, the triangles are similar. THEOREM III. 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. THEOREM IV. If two triangles...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 424 pages
...the tests of similarity is satisfied. PROP. XVII. THEOREM. 261. 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. A C B' Given, in A ABC and A'B'C', AC PBOP. XVIII....
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Examination Papers

University of Toronto - 1900 - 1160 pages
...proposition just after (IV. 10) 1 3. Equal triangles which have one augle of the i>ne equal to one 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...
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The Contents of the Fifth and Sixth Books of Euclid

Euclid, Micaiah John Muller Hill - Euclid's Elements - 1900 - 165 pages
...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 in the one equal to one angle in the other and the sides about...
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Examination Papers

University of Toronto - 1901 - 1192 pages
...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 fixed point P. On AB is described...
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