 If two triangles have two sides and the included angle of one equal to two sides and the included angle of the other, each to each, the other homologous parts are also equal, and the triangles are equal.  Elements of Geometry - Page 28by George Cunningham Edwards - 1895 - 293 pagesFull view - About this book
 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...= DF. The two triangles AGH, DEF, have the two sides and the included angle of the one respectively equal to two sides and the included angle of the other ; they are consequently equal. But the triangle AGH is similar to ABC; therefore DEF is also similar to ABC. THEOREM.... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...consequently the triangles ABF, HBC, have two sides and the included angle of the one respectively equal to two sides and the included angle of the other ; they are therefore equal (36). The triangle ABF is half of the rectangle BE], which has the same base BF and... | |
 | Adrien Marie Legendre - Geometry - 1825 - 276 pages
...= DF. The two triangles AGH, DEF, have the two sides and the included angle of the one respectively equal to two sides and the included angle of the other; they are consequently equal. But the triangle AGH is similar to ABC; therefore DEF is also similar to ABC. THEOREM.... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...occupied by the four right angles, as by the successive angles ACB, BCD, DCE, ECF, FCA. PROPOSITION V. THEOREM. ' If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...AH—DF. The two triangles AGH, DEF, have the two sides and the included angle of the one respectively equal to two sides and the included angle of the other ; they are consequently equal. But the triangle AGH is similar to ABC ; therefore DEF is also similar to ABC.... | |
 | Samuel Simon Schmucker - Psychology - 1842 - 262 pages
...known as Prop. IV. of Book I., viz. : If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, they must be identical or equal in all respects. For it virtually consists in supposing one of the two figures... | |
 | Anthony Dumond Stanley - Geometry - 1848 - 134 pages
...equal, the angles ACD and BCD subtended by them, are also equal ; and the triangles ACE, BCE, having two sides and the included angle of one equal to two sides and the included angle of the other, are every way equal, the side BE being equal to AE, and the angle EEC to the angle EAC... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...angles formed at the point of intersection, are together equal to four right angles. PROPOSITION VI. THEOREM. If two triangles have two sides, and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...occupied by the four right angles, as by the successive angles ACB, BCD, DCE, ECF. FCA. PROPOSITION V. THEOREM. If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each tc each, the two triangles will... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...(Ax. III.) And in the same manner it may be shown that the angle AFD is equal to BFC. PROPOSITION III. THEOREM. If two triangles have two sides and the included angle of the one, equal to the two sides and the included angle of the other, the triangles will be identical,... | |
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