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 - Σελίδα 45των Arthur Schultze, Frank Louis Sevenoak - 1902 - 370 σελίδεςΠλήρης προβολή - Σχετικά με αυτό το βιβλίο
| George Albert Wentworth, George Wentworth - 1912 - 602 σελίδες
...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 σελίδες
...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 - 1912 - 504 σελίδες
.... 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 - 1913 - 328 σελίδες
...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... | |
| Arthur Schultze, Frank Louis Sevenoak - 1913 - 486 σελίδες
...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 - 1913 - 491 σελίδες
...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... | |
| George Albert Wentworth, David Eugene Smith - 1913 - 496 σελίδες
...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 - 1914 - 236 σελίδες
...the A KP8 and A'Pi, /iP is common, PS = PL, (3) but KL < KS, (§ 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 - 1915 - 336 σελίδες
...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 - 1916 - 328 σελίδες
...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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