 If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.  Plane and Solid Geometry - Page 37by Wooster Woodruff Beman, David Eugene Smith - 1895 - 320 pagesFull view - About this book
 | 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 sides are, either... | |
 | James Andrew Blaikie, William Thomson - Geometry - 1891 - 160 pages
...triangle which has the greater contained angle shall be greater than the base of the other. 25. If two triangles have two sides of the one respectively equal to two sides of the other but the bases unequal, the angle contained by the two sides of the triangle which has the greater base... | |
 | Edward Travers Dixon - Geometry - 1891 - 180 pages
...angle opposite to it would be the less (see above), whereas it is the greater. PROPOSITION XIII. If two triangles have two sides of the one respectively equal to two sides of the other, but the angle between the directions of those sides greater in the one triangle than in the other,... | |
 | 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... | |
 | George Bruce Halsted - Geometry - 1896 - 208 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... | |
 | Queensland. Department of Public Instruction - Education - 1892 - 508 pages
...be careful to give the authority for each step. 10 2. Under what conditions are two triangles, which have two sides of the one respectively equal to two sides of the other, equal to one another ? 14 3. Give the enunciation and construction of I. II. 14 4. Prove that the parallelograms... | |
 | Euclid - Geometry - 1892 - 460 pages
...drawn: shew that the triangle BAX is equal to the triangle DAX. 9. If two triangles have two sides of one respectively equal to two sides of the other, and the angles contained by those sides supplementary, the triangles are equal in area. ON PROP. 39. 10. The straight... | |
 | William Chauvenet - 1893 - 340 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 angle.... | |
 | 1894 - 1136 pages
...if he had 8 less of each he would only have 6 geese for 7 ducks. How many had he of each ? 7. If two triangles have two sides of the one respectively equal to two sides of the other, but the contained • angles unequal, the base of the triangle which has the greater contained angle... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...placed among the axioms to be memorized, but it is equally an axiom nevertheless. ] Theorem 10. If two triangles have two sides of the one respectively equal to two sides of the other, but the included angles unequal, then the third sides are unequal, the greater side being opposite... | |
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