 | 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 the less AB; then,... | |
 | Adrien Marie Legendre - Geometry - 1822 - 394 pages
...specially assumed as the base, which is not equal to either of the other two. PROPOSITION XIII. THEOREM. Conversely, if two angles of a triangle are equal, the sides opposite them will be equal, and the triangle will be isosceles. LET the angle ABC be equal to ACB ; then will... | |
 | Adrien Marie Legendre - Geometry - 1838 - 382 pages
...generally assumed as the base, which is not equal to either of the other two. PROPOSITION XII. THEOREM. Conversely, if two angles of a triangle are equal, the sides opposite them are also equal, and the triangle is isosceles. Let the angle ABf be equal to the angle ACB ; then... | |
 | 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... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...generally assumed as the base, which is not equal to either of the other two. PROPOSITION XII. THEOREM. Conversely, if two angles of a triangle are equal, the sides opposite them are also equal, and the triangle is isosceles. Let the angle ABC be equal to the angle ACB; then... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...generally assumed as the base, which is not equal to either of the other two. PROPOSITION XII. THEOEEM. Conversely: If two angles of a triangle are equal, the sides opposite them are also equal, or, the triangle is isosceles. In the triangle BAC, let the angle B be equal to... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...generally assumed as the base, which is not equal to either of the other two. PROPOSITION XII. THEOREM. Conversely: If two angles of a triangle are equal, the sides opposite them are also equal, or, the triangle is isosceles. In the triangle BAC, let the angle B be equal to... | |
 | 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 AB C be... | |
 | 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 the... | |
 | 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 also equal... | |
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Conversely: if two angles of a triangle are equal, the sides opposite to them are equal, and the triangle it itosceles. 
