| Euclides - 1865 - 402 pages
...the three sides of a triangle to the opposite angles meet in the same point. 14. If two trapezinms **have an angle of the one equal to an angle of the other, and** if, also, the sides of the two figures, about each of their angles, be proportionals, the remaining... | |
| Benjamin Greenleaf - Geometry - 1868 - 338 pages
...properties of triangles 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 equal to the... | |
| Trinity College (Hartford, Conn.) - 1870 - 1010 pages
...arcs. 5. Prove that 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 - 316 pages
...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 two triangles having the... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...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 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 Chauvenet - Geometry - 1872 - 382 pages
...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 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... | |
| William Frothingham Bradbury - Geometry - 1872 - 256 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 - 286 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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