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. B' ADC A' D' C' Hyp. In triangles ABC and A'B'C', ZA = ZA'. Plane Geometry - Page 180by Arthur Schultze - 1901Full view - About this book
| Trinity College (Hartford, Conn.) - 1870 - 1008 pages
...equal the sum of the diagonals of the given quadrilateral. G. 4. Two triangles are similar, if they **have an angle of the one equal to an angle of the other** and the sides including those angles proportional. 5. In any triangle, if a straight line is drawn... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...GEOMETRY.— BOOK IV. THEOREMS. 219. Two triangles which have an angle of the one equal to the supplement of **an angle of the other are to each other as the products of the sides including the** supplementary angles. (IV. 22.) 220. Prove, geometrically, that the square described upon the sum of... | |
| 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... | |
| Henry William Watson - Geometry - 1871 - 320 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... | |
| William Chauvenet - Mathematics - 1872 - 382 pages
...GEOMETRY.— BOOK IV. THEOREMS. 219. Two triangles which have an angle of the one equal to the supplement of **an angle of the other are to each other as the products of the sides including the** supplementary angles. (IV. 22. ) 220. Prove, geometrically, that the square described upon the sum... | |
| 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... | |
| 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... | |
| Thomas Steadman Aldis - 1872 - 84 pages
...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,... | |
| 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... | |
| William Frothingham Bradbury - Geometry - 1872 - 262 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... | |
| |