 If two triangles have two sides of 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. 132- If two triangles have two sides of...  Plane Geometry - Page 71by Fletcher Durell, Elmer Ellsworth Arnold - 1917 - 318 pagesFull view - About this book
 | William James Milne - Geometry - 1899 - 326 pages
...&ABE + ДБ(Ж~ Д AED + &DEC; that is, AB CE - AECD. Ex. 540. Two triangles are equivalent, if they have two sides of one respectively equal to two sides of the other, and if the included angles are supplementary. Data : &ABC and BDC having AB = BD, BC in common, and Z ABC... | |
 | Euclid, Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...point X is taken, and XB, XD are 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... | |
 | Frederick Storrs Turner - Knowledge, Theory of - 1900 - 516 pages
...actual cases, consider the use of the law of Contradiction by Euclid. He takes two triangles which have two sides of one respectively equal to two sides of the other, and the included angles equal : on these data he argues that the third sides are equal. For supposing that one of the triangles... | |
 | 1900 - 650 pages
...angle is greater than the side which is opposite to the less. 6. Prove by a direct demonstration that if two triangles have two sides of one respectively equal to two sides of the other, but the base of one greater than the base of the other, the angle contained by the sides of that which... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...identically equal. PROPOSITION XX 79. If two triangles have two sides of the one equal, respectively, to two sides of the other, and the included angles...triangle which has the greater included angle has also the greater third side. Let ABC and A'B'C' be the two given triangles in which the side AB equals... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...hypotenuse from the vertex of the right angle. 8. Two triangles are equivalent if they have two sides of the one respectively equal to two sides of the other and the included angles a''e supplements of each other. 9. Two parallelograms are equivalent if two adjacent sides of one are... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...parallelogram into four equivalent triangles. Ex. 790. Two triangles are equivalent if two sides of the one are respectively equal to two sides of the other, and the included angles are supplementary. Ex. 791. The lines joining the midpoint of a diagonal of a quadriJateral with the... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...ABCDKF. PROPOSITION XXVIII. THEOREM 181. If two triangles have two sides of the one equal respectively to two sides of the other, and the included angles unequal, the third sides are unequal, and the greater third side belongs to the triangle having the greater included... | |
 | Charles Godfrey, Arthur Warry Siddons - Geometry - 1903 - 384 pages
...THEOREM 19.* If two triangles have two sides of the one equal to two sides of the other, each to each, and the included angles unequal, the triangle which...greater included angle has the greater third side. A CASE I. 8 CE fig. 142. Data ABC, DEF are two triangles which have AB = DE, and AC = DF but L BAC... | |
 | James McMahon - Geometry, Plane - 1903 - 382 pages
...Therefore the triangles ABC and A'B'C' are equal. Two sides and the angle opposite one. 97. THEOREM 20. If two triangles have two sides of one respectively equal to two sides of the other, and the angle opposite one of these equal to the corresponding angle in the other triangle, then the angles... | |
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