 | William Chauvenet, William Elwood Byerly - 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...of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side. Let ABC and ABD be the two... | |
 | 1887 - 644 pages
...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, William Elwood Byerly - 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 - 332 pages
...k IS EXERCISES ON BOOK IV. -f ( • ' \ [-:-" u3 THEOREMS. 1. Two" triangles are equivalent if they have two sides of the . 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... | |
 | 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... | |
 | 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... | |
 | James Wallace MacDonald - Geometry - 1889 - 80 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...of the other and the included angles unequal, the angle opposite the longer third side will be greater than the angle opposite the shorter. Proposition... | |
 | 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 - 160 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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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. 
