 | Pierre Simon marquis de Laplace, Thomas Young - Capillarity - 1821 - 402 pages
...CD=BE ; but 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... | |
 | 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... | |
 | 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 greater,... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...drawn from the vertex of an isosceles triangle to the middle of the base, bisects the vertical angle, and is perpendicular to the base. PROPOSITION XII....triangle is isosceles. In the triangle ABC, let the angle AB C be equal to the angle A CB : then will AC be equal to AB, and consequently, the triangle will... | |
 | 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... | |
 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...acute (257). 374. Corollary. — In a scalene triangle, no two angles are equal. EQUAL ANGLES. 375. Theorem. — If two angles of a triangle are equal, the sides opposite them are equal. For if these sides were unequal, the angles opposite to them would be unequal (272),... | |
 | 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 to the side... | |
 | Eli Todd Tappan - Geometry - 1868 - 444 pages
...acute (257). 274. Corollary — In a scalene triangle, no two angles are equal. EQUAL ANGLE8. 275. Theorem — If two angles of a triangle are equal, the sides opposite them are equal. For if these sides were unequal, the angles opposite to them would be unequal (272),... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1869 - 470 pages
...the middle of the base, bisects the vertical angle, and is perpendicular to the base. PROPOSITIOIT XII. THEOREM. If two angles of a triangle are equal,...triangle is isosceles. In the triangle ABC, let the angle AB C be equal to the angle A CB : then will AC be equal to AB, and consequently, the triangle will... | |
 | 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 greater,... | |
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THEOREM. If two angles of a triangle are equal, the sides opposite to them are also equal, and consequently, the triangle is isosceles. 
