 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 are equal in all respects.  Elements of Geometry - Page 45by Simon Newcomb - 1881 - 399 pagesFull view - About this book
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...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, or equal in all... | |
 | Charles Davies - Geometry - 1886 - 340 pages
...we have Of Triangles. ACD+BCD=ADC+BDC that is, the angle ACB=ADB. Now, the two triangles ACB and ADB have two sides and the included angle of the one equal to two sides and the in. eluded angle of the other, each to each: hence, the remaining angles will be equal (Th. iv) : consequently,... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...have, AB : DE :: AC : and by construction, AG=DE: hence, AH=DF. Therefore, the two triangles AGH, DEF, have two sides and the included angle of the one equal to the sides and the included angle of the other : hence, they are equal (B. L; p. 5) ; but the triangle... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...: DE : : AC : DF; and by construction, AG=DE : hence AN=DF. Therefore, the two triangles A GH, DEF, have two sides and the included angle of the one equal to twd sides and the included angle of the other: hence, they are equal (BI, p. 5); but the triangle AGH... | |
 | Samuel Simon Schmucker, S. S. (Samuel Simon) Schmucker - History - 1855 - 332 pages
...the nature, eg, of the demonstration of the theorem of Euclid known as Prop. IV. of Book I., viz.: If two triangles have two sides, and the included...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... | |
 | Charles Davies - Geometry - 1855 - 340 pages
...DEB (Ax- 3)In the same manner we may prove that the angle AED is equal to the angle CEBTHEOREM IV^ If two triangles have two sides and the included angle...the one, equal to two sides and the included angle of the o1l1er, each to each, the two triangles will be equalLet the triangles ABC and DEF have the... | |
 | Charles Davies, William Guy Peck - Electronic book - 1855 - 592 pages
...angles will also be equal, each to each, and the triangles themselves will bo equal." Prop. V. " When two triangles have two sides, and the included angle...the one equal to two sides and the included angle of the other, each to each, the two triangles will be equal. " Axiom 1. Things which are equal to the... | |
 | Mathematics - 1866 - 426 pages
...his Demonstration of I. G anything else ? by supposing BG = AC. he obtains two triangles having two sides and the included angle of the one equal to two sides and the included angle of the other ; two triangles, which, if the supposition BG = AG is correct should, applied one upon... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...line which has the sum of the interior angles less than two right angles. OF TRIANGLES. THEOREM XX. 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 fie identical, or equal in all... | |
 | Elias Loomis - Conic sections - 1857 - 242 pages
...equilateral. PROPOSITION XIII. THEOREM. If two triangles on equal spheres have two sides, and the tit. eluded angle of the one, equal to two sides and the included angle of the other, each to each, their third sides will be equal, and their other angles will be equal,... | |
| |
