 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.  Plane and Solid Geometry - Page 45by Arthur Schultze, Frank Louis Sevenoak - 1901 - 370 pagesFull view - About this book
 | George Albert Wentworth, George Wentworth - Geometry - 1912 - 602 pages
...the lines AB and CD, and at a distance of ^ in. from each of them. Exercise 16. Page 77 1 . If two triangles have two sides of the one equal respectively to two sides of the other, and the angles opposite two equal sides equal, the angles opposite the other two equal sides are 'equal... | |
 | Joseph Solomon - 1912 - 140 pages
...WilliarruTames," Contemporary Review, June, 1911. 233. the complete equality of two triangles that have two sides of the one equal respectively to two sides of the other and their included angles equal. But futurity, you say, is no illusion. I grant it. We feel time to... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
.... QED REASONS 1. In this case only three suppositions are admissible. 2. If two A have two sides of one equal respectively to two sides of the other, but the included Z of the first > the included Z. of the second, then the third side of the first > the third side of... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 pages
...and a point D in ^1.8 be taken so that ZACD>DCB, then AD>DB. PROPOSITION XXXII. THEOREM 133. If two triangles have two sides of the one equal respectively to two sides of the other, but the third side of the first greater than the third side of the second, PLANE GEOMETRY then the included... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 491 pages
...Now AP + PY>AY. Post. 3 .'. AP + PB>AY. Ax. 9 .'.AB>AY. Ax. 11 PROPOSITION XXIV. THEOREM 116. If two triangles have two sides of the one equal respectively to two sides of the other., but the third side of the first triangle greater than the third side of the second, then the angle opposite... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...ZB, and a point D in AB be taken so that ZACD>DCB, then AD>DB. PROPOSITION XXXII. THEOREM 133. If two triangles have two sides of the one equal respectively to two sides of the other, but the third side of the first greater than the third side of the second, then the included angle of the first... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...triangle to the mid-point of the opposite side is called a median of the triangle. EXERCISE 16 1. If two triangles have two sides of the one equal respectively to two sides of the other, and the angles opposite two equal sides equal, the angles opposite the other two equal sides are equal... | |
 | Sophia Foster Richardson - Geometry, Solid - 1914 - 236 pages
...the A KP8 and A'Pi, /iP is common, PS = PL, (3) but KL < KS, (ยง 96) and .-. Z. KPL < Z. KPS. (If two triangles have two sides of the one equal respectively to two sides of the other but the third side of the first less than the third side of the second, then the angle opposite the third side... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry, Plane - 1915 - 336 pages
...equal. Prove by the indirect method. 258. Theorem. // two triangles have two sides of one equal :r 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... | |
 | Jacob William Albert Young, Lambert Lincoln Jackson - Geometry, Plane - 1916 - 328 pages
...Square -E. PROPOSITION XV. THEOREM 121. If two triangles have two sides of the one respectively equal to two sides of the other, but the included angle...of the second, then the third side of the first is longer than the third side of the second. FIG. 1 FIG. 2 Given AB = DE, BC = EF aud ZB > Z E. To prove... | |
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