| 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... | |
| 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 of the other,** and the third sides unequal, the triangle which has the greater third side has the greater included... | |
| 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... | |
| James Wallace MacDonald - Geometry - 1894 - 76 pages
...triangle having sides equal to the sides of a given triangle. Proposition XXXI. A Theorem. 68. If two **triangles have two sides of the one respectively equal to two sides of the other** and the included angles unequal, the third side of the one having the greater angle will be longer... | |
| 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 to two sides of the other** and the included angles unequal, the angle opposite the longer third side will be greater than the... | |
| 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... | |
| James Blaikie, William Thomson - Geometry - 1891 - 160 pages
...I. 38 to show AABD = AACD, AGBD = AGCD; ... AGAB = AGCA; .'. their halves are equal, etc. 7. If two **triangles have two sides of the one respectively equal to two sides of the other** and the contained angles supplementary, the triangles shall be equal in area. Place the triangles so... | |
| Edward Travers Dixon - Geometry - 1891 - 180 pages
...equal to them of the other triangle. Hence the triangles are congruent. [I. 10. PROPOSITION XV. If two **triangles have two sides of the one respectively equal to two sides of the other,** and an angle of the one triangle opposite one of those sides equal to that opposite the equal side... | |
| Seth Thayer Stewart - Geometry, Modern - 1891 - 428 pages
...opposite these sides in the other, are equal in all their parts. (Same.) Corollary IV. Two triangles, with **two sides of the one respectively equal to two sides of the other, the** two angles opposite these sides, in each triangle, being both acute, or one acute and the other obtuse,... | |
| George Bruce Halsted - Geometry - 1896 - 204 pages
...third, that cutting the axis is the greater. Proof. BA = BC + CA' ; BC+ CA > BA'. 304. Theorem. If two **triangles have two sides of the one respectively equal to two sides of the other,** but the included angles unequal, then that third side is the greater which is opposite the greater... | |
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