 | 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... | |
 | Adrien Marie Legendre - Geometry - 1822 - 394 pages
...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 the... | |
 | Adrien Marie Legendre - Geometry - 1838 - 382 pages
...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 will... | |
 | Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...and then the vertex is the vertex of the opposite angle. PROP. VII. THEOREM. (Converee of Prop. VI.) If two angles of a triangle are equal, the sides opposite them are also equal, and the triangle is isosceles. In the triangle ABC, let the angles ABC, BAC, be equal,... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...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 will the... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...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 the angle... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...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 the angle... | |
 | William E. Bell - Bridge building - 1857 - 250 pages
...middle point, for the two angles at D are each right angles. (Prop. X.) Proposition XVIII. Theorem. When two angles of a triangle are equal, the sides opposite them are also equal, and the triangle is isosceles. Let the angle A=B, then will the sides AC and BC be equal... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...middle 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... | |
 | 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,...unequal (272), which is contrary to the hypothesis. 376. Corollary. — If a triangle is equiangular, that is, has all its angles equal, then it is equilateral.... | |
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Conversely, if two angles of a triangle are equal, the sides opposite them are also equal, and the triangle is isosceles. 
