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 146by Benjamin Peirce - 1871 - 150 pagesFull view - About this book
| 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... | |
| 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.... | |
| 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... | |
| 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... | |
| 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 - 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 =... | |
| 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 - 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... | |
| 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... | |
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