 If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.  The Elements of Geometry - Page 44by George Bruce Halsted - 1885 - 366 pagesFull view - About this book
 | Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...direction. To prove the proposition by the help of the construction we must know, — 1. That if two AS have two sides of the one equal respectively to two sides of the other, and also the ^ included between the said sides in the first A equal to the ^ included between the said... | |
 | George Albert Wentworth - Geometry - 1877 - 426 pages
...two sides of the one equal respectively to two sides of the other, but the included angle of thefirst greater than the included angle of the second, then...will be greater than the third side of the second. B E la the AAB С and ABE, let AB = AB, but Z ABO Z ABE. We are to prove A С > A E. Place the A so... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...equiangular triangle is also equilateral. OEOMETRY. BOOK I. PROPOSITION XXXI. THEOREM. 115. If two triangles have two sides of the one equal respectively...two sides of the other, but the included angle of tlie first greater than the included angle of the second, then the third side of the first will be... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...equiangular triangle is also equilateral. GEOMETRY. BOOK I. PROPOSITION XXXI. THEOREM. 115. If two triangles have two sides of the one equal respectively...to two sides of the other, but the included angle (f the first greater than the included angle of the second, then 1lie third side of the first will... | |
 | George Albert Wentworth - Geometry - 1877 - 436 pages
...of the other two sides of the triangle. 2. On the same sphere, or on equal spheres, if two spherical triangles have two sides of the one equal respectively to two sides of the other, hut the included angle of the first greater than the included angle of the second, then the third side... | |
 | Robert Fowler Leighton - 1877 - 372 pages
...that when two triangles have two sides of the one respectively equal to two sides of the other and 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. 3. Show how to draw a tangent... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...triangle is also equilateral. 50 (1EOMKTRY. BOOK I. PROPOSITION XXXI. THEOREM. 115. If two triangles hare two sides of the one equal respectively to two sides of the oiher, but the included angle of the first greater than the included angle of the second, then the... | |
 | George Albert Wentworth - 1879 - 196 pages
...inequalities, BD _f. DC< AB .f AC. Ex. 2. On the same sphere, or on equal spheres, if two spherical triangles have two sides of the one equal respectively...will be greater than the third side of the second. In the spherical A ABC and A'B'C, let AB = A'B',AC = AC,ZA>£A'; then is BC> B'C. If the parts are... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...parallelogram ; E and F the middle points of AB and CD. BF and ED trisect the diagonal A G. 104. If two triangles have two sides of the one equal respectively to two sides of the other, and the included angles supplementary, the triangles are equivalent. 105. The diagonals divide a parallelogram... | |
 | George Albert Wentworth - 1881 - 266 pages
...QED Ex. Show that an equiangular triangle is also equilateral. PROPOSITION XXXI. THEOREM. 115. If two triangles have two sides of the one equal respectively...will be greater than the third side of the second. BB В In the А ABC and ABE, let AB = AB, BC — BЕ; but ¿ABO ¿ ABE. We are to prove A С > A E.... | |
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