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" Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar. "
The Elements of geometry; or, The first six books, with the eleventh and ... - Pagina 143
door Euclides - 1855
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1871 - 368 pagina’s
...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 an angle...
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The Elements of Plane and Solid Geometry

Henry William Watson - 1871 - 285 pagina’s
...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...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1872 - 368 pagina’s
...an angle of the 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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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1872 - 368 pagina’s
...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 an angle...
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Euclid's Elements of Geometry

Euclid - 1872 - 261 pagina’s
...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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Text book of geometry, Deel 2

Thomas Steadman Aldis - 1872
...diagonals proportionals, each to each, prove that they are similar. THEOREM XIII. If two triangles have an angle of the one equal to an angle of the other, and the sides about the equal angles proportional, they shall be similar. Let ABC and PQR be two triangles,...
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An Elementary Geometry

William Frothingham Bradbury - 1872 - 110 pagina’s
...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...
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - 1872 - 238 pagina’s
...(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...
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Mensuration of lines, surfaces, and volumes

David Munn - 1873
...on it from the opposite angles 42 VII. To find the area of any polygon 43 EXERCISES (4) 44 VIII. 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 47 IX. The areas of similar triangles...
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New Elementary Geometry: Ith Practical Applications; a Shorter Course Upon ...

Benjamin Greenleaf - 1873 - 176 pagina’s
...the triangle ABC; hence the triangles DEF, ABC are also equiangular and similar. THEOREM XV. 208. 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, DEF have...
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