| Trinity College (Hartford, Conn.) - 1870 - 1008 pages
...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... | |
| Henry William Watson - Geometry - 1871 - 320 pages
...similar to 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... | |
| 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... | |
| 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... | |
| William Frothingham Bradbury - Geometry - 1872 - 268 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 =... | |
| 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... | |
| Euclid - Geometry - 1872 - 284 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... | |
| 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, b« the two triangles having the... | |
| Thomas Steadman Aldis - 1872 - 84 pages
...of "proportional compasses." 2. Two triangles have their altitudes proportional to their bases, and **an angle of the one equal to an angle of the other,** adjacent to the bases; prove that they are similar. 3. Prove that two quadrilateral figures are similar... | |
| William Chauvenet - Mathematics - 1872 - 382 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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