| Franklin Ibach - Geometry - 1882 - 208 pages
...the equal angles lie opposite the equal sides. ELEMENTS OF PLANE GEOMETRY. THEOREM XXVII. 89. If two **triangles have two sides of the one respectively equal to two sides of the other, and the included** angles unequal, the third sides are unequal, and the greater third side is in the triangle having the... | |
| Simon Newcomb - Trigonometry - 1882 - 372 pages
...Altitude A = b sin y. Therefore, a being the base, "/ ' Area = \ah = \ab sin y. QED Cor. 1. If two **triangles have two sides of the one respectively equal to two sides of the other, and the** angles which these sides form supplementary, the triangles will be equal in area. For the sines of... | |
| 1882 - 376 pages
...Ans.—£2112. GEOMETRY. Examiners—Prof. AG GREENHILL, MA, and BENJAMIN WILLIAMSON, Esq., MA, FRS 1. If two **triangles have two sides of the one respectively equal to two sides of the other,** but the contained angle of the one greater than the contained angle of the other, prove that the base... | |
| Edward Olney - Geometry - 1883 - 354 pages
...triangles, the equal angles lie opposite the equal sides. PROPOSITION VIII. 307. Theorem.— If two **triangles have two sides of the one respectively equal to two sides of the other, and the included** angles unequal, the third sides are unequal, and the greater third side belongs to the triangle having... | |
| Euclides - 1884 - 434 pages
...construction as in the text, but let A DEO fall on the other side of DE. PROPOSITION 25. THEOREM. If two **triangles have two sides of the one respectively equal to two sides of the other,** but their bases unequal, the angle contained by the two sides of the triangle which has the greater... | |
| Public schools - 1884
...Prove that if two triangles have two sides of the one equal respectively to two sides of the other, but **the included angle of the first greater than the included angle of the second,** then the third side of the first is greater than the third side of the second. 8. Prove that if the... | |
| George Bruce Halsted - Geometry - 1885 - 389 pages
...opposite equal sides are equal.) But £ BDA -f 2£ ^C = st. £, = st. :£. 178. COROLLARY I. If two **triangles have two sides of the one respectively equal to two sides of the other, and the** angles opposite to one pair of equal sides equal, then, if one of the angles opposite the other pair... | |
| Webster Wells - Geometry - 1886 - 392 pages
...THEOREM. 86. If two triangles have two sides of one equal respectively to two sides of the other, but **the included angle of the first greater than the included angle of the second, the third side of the first** is greater than the third side of the second. In the triangles ABC and DEF, let the side AB be equal... | |
| George Bruce Halsted - Geometry - 1886 - 394 pages
...angles opposite equal sides are equal.) But £ BDA + 4 BDC = st. £, = st. . 178. COROLLARY I. If two **triangles have two sides of the one respectively equal to two sides of the other, and the** angles opposite to one pair of equal sides equal, then, if one of the angles opposite the other pair... | |
| William Chauvenet - Geometry - 1887 - 332 pages
...k IS EXERCISES ON BOOK IV. -f ( • ' \ [-:-" u3 THEOREMS. 1. Two" triangles are equivalent if they **have two sides of the . one respectively equal to...sides of the other, and the included angle of the** one equal to the supplement of the included angle of the other. 2. The two opposite triangles formed... | |
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