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" 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. "
Gradations in Euclid : books i. and ii., with an explanatory preface [&c ... - Page 93
by Euclides - 1858
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Elements of Geometry with Exercises for Students: An an Introduction to ...

Aaron Schuyler - Geometry - 1876 - 384 pages
...B = E (53, 5), and the triangles are equal, as just shown. 73. Proposition XXIX.— Theorem. If two triangles have two sides of the one respectively equal to two sides of the other, and the included angle of the one greater than the included angle of the other, the third side of the...
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A Treatise on Special Or Elementary Geometry

Edward Olney - Geometry - 1877 - 272 pages
...secured by bringing together the two greatest sides. PROPOSITION X. Fio. 210. 295. Theorem.—If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the third sides are unequal, and the greater third side belongs to...
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Exercises on Euclid and in modern geometry, New ed., revised

James McDowell - 1878 - 312 pages
...angle. CoR 19 25. Given the three bisectors of the sides of a triangle ; construct it. DBF 20 26. If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, they are equal in area 20 27. If squares be described on the...
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Gibson's London matriculation guide, by J. Gibson [and others].

1882 - 376 pages
...Ans.—2112. GEOMETRY. Examiners—Prof. AG GREENHILL, MA, and BENJAMIN WILLIAMSON, Esq., MA, FRS 1. If two triangles have two sides of the one respectively equal to two sides of the other, but the contained angle of the one greater than the contained angle of the other, prove that the base...
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Elements of Plane and Spherical Trigonometry with Logarithmic and Other ...

Simon Newcomb - Trigonometry - 1882 - 372 pages
...Altitude A = b sin y. Therefore, a being the base, "/ ' Area = \ah = \ab sin y. QED Cor. 1. If two triangles have two sides of the one respectively equal to two sides of the other, and the angles which these sides form supplementary, the triangles will be equal in area. For the sines...
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Elements of Plane Geometry

Franklin Ibach - Geometry - 1882 - 208 pages
...the equal angles lie opposite the equal sides. ELEMENTS OF PLANE GEOMETRY. THEOREM XXVII. 89. If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the third sides are unequal, and the greater third side is in the...
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Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with ...

Edward Olney - Geometry - 1883 - 354 pages
...triangles, the equal angles lie opposite the equal sides. PROPOSITION VIII. 307. Theorem.— If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the third sides are unequal, and the greater third side belongs to...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884 - 434 pages
...construction as in the text, but let A DEO fall on the other side of DE. PROPOSITION 25. THEOREM. If two triangles have two sides of the one respectively equal to two sides of the other, but their bases unequal, the angle contained by the two sides of the triangle which has the greater...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1885 - 389 pages
...opposite equal sides are equal.) But BDA -f 2 ^C = st. , = st. :. 178. COROLLARY I. 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, if one of the angles opposite the other...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1886 - 394 pages
...angles opposite equal sides are equal.) But BDA + 4 BDC = st. , = st. . 178. COROLLARY I. 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, if one of the angles opposite the other...
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