 | War office - 1861 - 714 pages
...(f )2 to a decimal fraction. 10. Extract the square root of 4-20291001. Euclid. 1. If two triangles have two angles of the one equal to two angles of the other, each to each, and the side adjacent to the equal aii'/les in each triangle also equal, then shall the other sides... | |
 | War office - 1861 - 260 pages
...sovereign and a shilling ? MATHEMATICS. Voluntary Paper, No. II. REV. WN GRIFFIN, MA 1. If two triangles have two angles of the one equal to two angles of the other, and one side equal to one side, namely, the sides which are opposite to equal angles in each, then... | |
 | Benjamin Greenleaf - Geometry - 1862 - 514 pages
...equal to the right angle EF С (Art. 34, Ax. 9) ; therefore GFE is equal to G С F, or DFE to В С А. Therefore the triangles ABC, DEF have two angles of...each ; hence they are similar (Prop. XXII. Cor.). 206. Scholium. When the two triangles have their sides parallel, the parallel sides are homologous... | |
 | Euclides - 1862 - 140 pages
...EDF. Conclusion. — Therefore, if two triangles, &c. QED PROPOSITION 26.— THEOREM. If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side; namely, either the side adjacent to the equal angles in sach, or the... | |
 | Benjamin Greenleaf - Geometry - 1861 - 628 pages
...proportional ; and consequently the two triangles are similar (Art. 210). 260. Cor. Two triangles having two angles of the one equal to two angles of the other, each to each, are similar ; since the third angles will also be equal, and the two triangles be equiangular. 261.... | |
 | Benjamin Greenleaf - Geometry - 1862 - 520 pages
...proportional ; and consequently the two triangles are similar (Art. 210). 260. Cor. Two triangles having two angles of the one equal to two angles of the other, each to each, are similar ; since the third angles will also be equal, and the two triangles be equiangular. 261.... | |
 | Benjamin Greenleaf - Geometry - 1863 - 502 pages
...together equal to two right angles (Prop. I. Bk. I.) ; hence the angle EDF is equal to BAG or BAC. B The two angles, GFC, GCF, in the right-angled triangle...Cor.). homologous. Thus, DE is homologous with AB, DP with AC, and EF with B C. PROPOSITION XXYI. — THEOREM. 267. In any triangle, if a line be drawn... | |
 | Euclides - 1863 - 122 pages
...and the right angle BED (I. Ax. 11) to the right angle BFD. Therefore the two triangles E BD and FBD have two angles of the one equal to two angles of the other, each to each ; and the side BD, which is opposite to one of the equal angles in each, is common to both. Therefore... | |
 | Euclides - 1884 - 214 pages
...sixteenth, it would be a proof of both the sixteenth and seventeenth. It shows us that, if two triangles have two angles of the one equal to two angles of the other, each to each or together, their third angles are also equal. The corollaries to this proposition are not Euclid's.... | |
 | Mathematical association - 1884 - 146 pages
...that the straight line joining their vertices bisects the vertical angles. THEOR. 19. If two triangles have two angles of the one equal to two angles of the other, each to each, and have likewise the sides opposite to one pair of equal angles equal, then the triangles are identically... | |
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If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent. 
