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" The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C'... "
An Elementary Treatise on Plane and Solid Geometry - Page 146
by Benjamin Peirce - 1871 - 150 pages
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - 1868 - 338 pages
...include, by implication, those of all figures. PROPOSITION XXIV. — THEOREM. 264. Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing these angles proportional, are similar. Let the two triangles ABC, PEF have the angle A...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1869 - 150 pages
...whence the triangle ABC — the triangle DEF. 467. Corollary. Hence all spherical triangles, which Area of a Spherical Triangle. are equilateral or equiangular...supplements of those which include it in the other triangle ; the sum of the surfaces of the two triangles is measured by double the included angle. Proof....
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Catalogue of the Officers and Students

Trinity College (Hartford, Conn.) - 1870
...parallelograms which have equal bases and equal altitudes are equal. G. Prove that two triangles which have an angle of the one equal to an angle of the other are to each other as the rectangles of the including sides. ENGLISH. I. Correct, criticize, and recast...
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The Elements of Plane and Solid Geometry

Henry William Watson - Geometry - 1871 - 285 pages
...the triangle AGH, therefore the triangle ABC is similar to the triangle DEF. PROPOSITION 18. If two triangles have an angle of the one equal to an angle of the other, and the sides containing those angles proportionals, the triangles shall be similar. Fig. 25. Let ABC and DEF be...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...other are to each other as the products of the sides including the equal angles. Two triangles which have an angle of the one equal to an angle of the other may be placed with their equal angles in coincidence. Let ABC, ADE, be the two triangles having the...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...of the ratio of similitude of the triangles. PROPOSITION VIII.— THEOREM. 22. Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. Two triangles which have...
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1872 - 238 pages
...(I. 35^, and similar (20) ; therefore BG:EH—AB:DE=AC:DF=BC:EF THEOREM X. 23, Two triangles having an angle of the one equal to an angle of the other, and the sides including these angles proportional, are similar. E D In the triangles ABC, DEF let t!:e angle A =...
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An Elementary Geometry

William Frothingham Bradbury - Geometry - 1872 - 124 pages
...DEH are equiangular (I. 35), and similar (20) ; therefore : EF D THEOREM X. 231 Two triangles having an angle of the one equal to an angle of the other, and the sides including these angles proportional, are similar. In the triangles ABC,DEF let tiifl angle A =: D and...
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Euclid's Elements of Geometry

Euclid - Geometry - 1872 - 261 pages
...be right, the remaining angles will be right angles. FIRST BOOK. COR. 2. — If two parallelograms have an angle of the one equal to an angle of the other, the remaining angles will be also equal ; for the angles which are opposite to these equal angles are...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...other are to each other as the products of the sides including the equal angles. Two triangles which have an angle of the one equal to an angle of the other may be placed with their equal angles in coincidence. Let ABC, ADE, bę the two triangles having the...
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