| Cambridge univ, exam. papers - 1856
...on the same side of it, are either two right angles, or are together equal to two right angles. 3. **If two triangles have two angles of the one equal to two angles of the other, each to each, and one** si ie equal to one side, via. the sides opposite to equal angles in each, then shall the other sides... | |
| Peter Nicholson - 1856 - 216 páginas
...parallel to CD, the alternate angles, GFE, FGH, are also equal ; therefore the two triangles GEF, HFG, **have two angles of the one equal to two angles of the other, each to each ; and** the side FG, adjacent to the equal angles, common ; the triangles are therefore equal (theorem 6) ;... | |
| Euclides - 1856
...BAC, and the angle ABE is equal to the angle ABC (being both right angles), the triangles ABC, ABE **have two angles of the one equal to two angles of the other,** and the side AB common to the two. Therefore the triangles ABC, ABE are equal, and the side AE is equal... | |
| Elias Loomis - 1857 - 226 páginas
...is parallel to CD, the alternate angles GHE, HEF are also equal. Therefore, the triangles HEF, EHG **have two angles of the one equal to two angles of the other, each to each, and** the side Eli included between the equal angles, common ; hence the triangles are equal (Prop. VII.)... | |
| Adrien Marie Legendre - 1857 - 448 páginas
...consequently, the two equiangular triangles BA C, CUD, are similar figures. Cor. Two triangles which **have two angles of the one equal to two angles of the other,** are similar; for, the third angles are then equal, and the two triangles are equian gular (BI, p. 25,... | |
| Euclides - 1858
...to assist in the demonstration of the following propositions. PROP. 26.— THEOR. — (Important.) **If two triangles have two angles of the one equal...other, each to each, and one side equal to one side,** viz., either the sides adjacent to the equal angles in each, or the sides opposite to them, then shall... | |
| Elias Loomis - 1858 - 234 páginas
...is parallel to CD, the alternate angles GHE, HEF are also equal. Therefore, the triangles HEF, EHG **have two angles of the one equal to two angles of the other, each to each, and** the side Eli included between the equal angles, common ; hence the triangles are equal (Prop. VII.)... | |
| William Ernest Johnson - 1889 - 504 páginas
...draw IX, IT, IZ perpendiculars on the sides. Then, the triangles BXI, BZ1 having a common side BI and **two angles of the one equal to two angles of the other,** are equal in all respects, so that IX=IZ. Similarly IX=IY, :.IY=IZ. Therefore, the triangles AZI, A... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 515 páginas
...Write down the obverse of Prop. 8. From what Proposition is it an immediate inference ? PROPOSITION 26. **THEOREM. If two triangles have two angles of the one...other, each to each, and one side equal to one side,** namely, either the sides adjacent to the equal angles or sides which are opposite to equal angles in... | |
| Euclid - 1890 - 400 páginas
...D, for this necessitates that BC < EF. AA It remains .'. that A > D. Proposition 26. (First Part.) **THEOREM — If two triangles have two angles of the...equal to two angles of the other, each to each, and** have likewise the two sides adjacent to these angles equal ; then the triangles are identically equal,... | |
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