 | George Albert Wentworth - 1881 - 266 pages
...But . AE - EH '•= Wo'' A'B' ~ We'Hyp. Ax. 1 Since AE = A' B', Cons. PROPOSITION VI. THEOREM. 284. Two triangles having an angle of the one equal to an angle of the other, and the including sides proportional, are similar. A A' In the triangles ABC and A' B' C' let -. A'B'... | |
 | George Albert Wentworth - Geometry, Modern - 1882 - 268 pages
...to the sum of the squares on the diagonals. GEOMETRY. — BOOK IV. PROPOSITION XIII. THEOREM. 341. Two triangles having an angle of the one equal to...products of the sides including the equal angles. Let the triangles ABC and AD E have the common angle A. TT . АABС We are to prove AB X AC Draw B... | |
 | George Albert Wentworth - Geometry, Modern - 1879 - 262 pages
...the squares on the diagonals. PEOPOSITION XIII. THEOREM. 341. Two triangles having an angle of ihe one equal to an angle of the other are to each other as the products of 1 fie sides including the egtial angles. Let the triangles ABC and AD E have the common angle A.... | |
 | Franklin Ibach - Geometry - 1882 - 208 pages
...AD or AC* : ~B(? :: AD : BD. THEOREM XXIV. 284. Two triangles having an angle in each the same are to each other as the products of the sides including the equal angles. In the As ABC and DEC let the angle c be common. 0 To prove that A ABC : A DEC :: CA X CB : CD X CE.... | |
 | Great Britain. Education Department. Department of Science and Art - 1882 - 510 pages
...values attached to the questions differ little from one another. 1. Prove that two triangles, which have an angle of the one equal to an angle of the other, and the sides including the equal angles proportional, are similar. A diagonal of a parallelogram is... | |
 | Mathematical association - 1883 - 86 pages
...two adjoining sides of the one respectively equal to two adjoining sides of the other, and likewise an angle of the one equal to an angle of the other; the parallelograms are identically equal. [By Superposition.] COR. Two rectangles are equal, if two... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 170 pages
...construction similar to DGE; hence, it is also similar to DFE. Therefore, two triangles, etc. THEOREM XI. Two triangles having an angle of the one equal to an angle of the other, and the sides about those angles proportional, are similar. Let the two triangles ABC, DEF, have the... | |
 | George Albert Wentworth - 1884 - 264 pages
...radius of the circle. COMPARISON OP AREAS. 187. Theorem. The areas of two triangles having an angle of one equal to an angle of the other are to each other as the rectangles of the sides including the equal angles. 188. Theorem. Similar triangles are to each other... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 242 pages
...EAJ (?). Complete. 12. Two tetraedrons, which have a triedral angle of the one equal to a triedral angle of the other, are to each other as the products of the three edges of the equal diedrals. A-BCDandA'-BC'D' A are the tetraedrons having a common triedral,... | |
 | Mathematical association - 1884 - 146 pages
...two adjoining: sides of the one respectively equal to two adjoining sides of the other, and likewise an ang:le of the one equal to an angle of the other ; the parallelograms are identically equal. Let ABCD, EFGH be two parallelograms having the angle ABC... | |
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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. 
