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" If two triangles have two sides of one respectively equal to two sides of the other, but the third sides unequal... "
An Elementary Geometry - Page 23
by William Frothingham Bradbury - 1872 - 110 pages
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Plane Geometry

William James Milne - Geometry, Modern - 1899 - 258 pages
...divide the quadrilateral into two equivalent parts. 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. /' Ex. 541. 0 is any point on the diagonal AC -of the...
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Key to Milne's Plane and Solid Geometry

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...
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Plane and Solid Geometry

William James Milne - Geometry - 1899 - 398 pages
...divide the quadrilateral into two equivalent parts. 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. Ex. 541. O is any point on the diagonal AC of the parallelogram...
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Annual Report of the Commissioners ..., Volume 66

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 has...
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A Text-book of Euclid's Elements for the Use of Schools. Books I.-VI ..., Book 1

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....
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Knowledge, Belief and Certitude: An Inquiry with Conclusions

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...
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Elementary Geometry: Plane

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...
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Elementary Geometry: Plane

James McMahon - Geometry, Plane - 1903 - 380 pages
...path of P. To prove that this line is actually fixed in position as P moves. The triangles POM, PON have two sides of one respectively equal to two sides of the other, and the angles opposite a pair of equal sides are right angles ; therefore the angles POM and PON are...
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A Text-book of Euclid's Elements for the Use of Schools, Book 1

Euclid - Euclid's Elements - 1904 - 488 pages
...XB, XD are drawn : shew that the triangle BAX is equal to the triangle DAX. 9. If two triangles hajve 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....
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Plane and Solid Geometry

Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...be deduced immediately from Theorem IX? Also Corollary II, 97 from Theorem VIII? THEOREM X 130. 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...
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