 | Pierre Simon marquis de Laplace, Thomas Young - Capillarity - 1821 - 402 pages
...BD=CE (16), therefore L BCDz=CBE (86), and L ACD— BCD=ABE— CBE (16), or L ACB=ABC. 88. THEOREM. If two angles of a triangle are equal, the sides opposite to them are equal. Let L ABCizBCD ; then AC=AB. If it bo denied, take, in the greater AC, CD equal to... | |
 | Anna Cabot Lowell - Geometry - 1846 - 216 pages
...erected upon the middle point of the base of an isosceles triangle, bisects the opposite angle. 134. If two angles of a triangle are equal, the sides opposite to these angles are also equal. Dem. (fig. 86.) Let angle A = B. Upon the middle point of the base AB erect a perpendicular to AB.... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...\_ B. Hence the theorem ; if two sides of a triangle are equal, the angles, etc. Cor. 1. Conversely: if two angles of a triangle are equal, the sides opposite to them are equal, and the triangle it itosceles. For, if AC is not equal to BC, suppose BC to be trie... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...of the base, bisects the vertical angle, and is perpendicular to the base. PROPOSITION XII. THEOREM. If two angles of a triangle are equal, the sides opposite , to them are also equal, and consequently, the triangle is isosceles. In the triangle ABC, let the angle... | |
 | Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...still more, then, is it greater than BAG. Therefore, the greater of two unequal sides, etc. Cor. Hence, if two angles of a triangle are equal, the sides opposite to them can not be unequal. THEOREM X. If two triangles have two sides of the one equal to two sides of... | |
 | Euclides - 1865 - 80 pages
...ACB. Cor. Hence the less angle of every triangle is opposite to the less side. PROPOSITION XIX. THEOR. If two angles of a triangle are equal, the sides opposite to them are also equal. Let ABC be a triangle having the angle B equal to the angle C, the side AB is... | |
 | Isaac Todhunter - Measurement - 1869 - 312 pages
...Art. 18. 24. Jf two sides of a triangle are equal the angles opposite to them will also be equal. 25. If two angles of a triangle are equal the sides opposite to them will also be equal. 26. Iftico sides of one triangle are equal to two sides of another, each to... | |
 | Horatio Nelson Robinson - 1869 - 276 pages
...[_B. Hence the theorem; if two sides of a triangle are equal, the angles, etc. Cor. 1. Conversely: if two angles of a triangle are equal, the sides opposite to them are equal, and the triangle is isosceles. For, if AC is not equal to BC, suppose BC to be the... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...than the angle B (69) ; still more, then, is A CB greater than B. PROPOSITION XXVII.— THEOREM. 90. If two angles of a triangle are equal, the sides opposite to them are equal. In the triangle ABC, let the angles B and C be equal ; then, the sides AB and AC are... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...than the angle B (69); still more, then, is A CB greater than B. PROPOSITION XXVII.— THEOREM. 90. If two angles of a triangle are equal, the sides opposite to them are equal. In the triangle ABC, let the angles B and C be equal ; then, the sides AB and AC are... | |
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If two angles of a triangle are equal, the sides opposite to these angles are equal 21 ^THEOREM 14. 
