| 1887
...sq. on AB," and for "the rectangle contained by the straight lines AB, CD"is"rect. AB, CD." 1. If two **triangles have two sides of the one respectively equal to two sides of the other and the included** angles equal, the remaining sides shall be equal. 2. If two triangles have two sides of the one respectively... | |
| William Chauvenet - Geometry - 1887 - 336 pages
...than BC, by Proposition XII. Therefore C is greater than A. PROPOSITION XIV.— THEOREM. 30. If two **triangles have two sides of the one respectively equal to two sides of the other, and the included** angles unequal, the triangle which has the greater included angle has the greater third side. Let ABC... | |
| William Chauvenet - Geometry - 1887 - 331 pages
...and substituting EC for its equal ED, BE + EC > BD, or BC > BD. PROPOSITION XV.—THEOREM. 31. If two **triangles have two sides of the one respectively equal to two sides of the other, and the** third sides unequal, the triangle which has the greater third side has the greater included angle.... | |
| William Chauvenet, William Elwood Byerly - Geometry - 1887 - 342 pages
...triangle which has the greater included angle has the greater third side. PROPOSITION XV. If two triangle* **have two sides of the one respectively equal to two sides of the other, and the** third sides unequal, the triangle which has the greater third side has the greater included angle.... | |
| William Chauvenet - Geometry - 1887 - 336 pages
...43.) 13 EXERCISES ON BOOK IV. THEOREMS. 1. Two triangles are equivalent if they have two sides of th« **one respectively equal to two sides of the other, and the included angle of the** one equal to the supplement of the included angle of the other. 2. The two opposite triangles formed... | |
| William Chauvenet - Geometry - 1887 - 346 pages
...the triangle which has the greater included angle has the greater third side. PROPOSITION XV. If two **triangles have two sides of the one respectively equal to two sides** uf the cither, and the third sides unequal, the triangle which has the greater third side has the greater... | |
| George Albert Wentworth - Geometry - 1888 - 274 pages
...THEOREM. 152. // two triangles have two sides of the one equal respectively to two sides of the other, but **the included angle of the first greater than the included angle of the second,** then the third side of the first will be greater than the third side of the second. 111 'the triangles... | |
| James Wallace MacDonald - Geometry - 1889 - 63 pages
...Three different cases may arise ; prove each. Proposition XXXII. A Theorem. 69. Conversely, if two **triangles have two sides of the one respectively equal to two sides of the other and the included** angles unequal, the angle opposite the longer third side will be greater than the angle opposite the... | |
| James Wallace MacDonald - Geometry - 1894 - 76 pages
...Three different cases may arise ; prove each. Proposition XXXII. A Theorem. 69. Conversely, if two **triangles have two sides of the one respectively equal to two sides of the other and the** third sides unequal, the angle opposite the longer third side will be greater than the angle opposite... | |
| Robert Baldwin Hayward - Geometry, Solid - 1890 - 130 pages
...Hence prove VIII. 4 directly without the aid of the polar triangles. X. — Ambiguous Cases. 1 . If two **triangles have two sides of the one respectively equal to two sides of the other and the** angles opposite to one pair of equal sides equal, then the angles opposite to the other pair of equal... | |
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