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" If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second.... "
Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ... - Page 28
by George Roberts Perkins - 1856 - 235 pages
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Elements of Geometry with Exercises for Students: An an Introduction to ...

Aaron Schuyler - Geometry - 1876 - 384 pages
...- = GF, BG+GC>BF. But, BG + GC •= BC, and BF = EF, BC>EF. 74. Proposition XXX.— Theorem. If two triangles have two sides of the one respectively equal to two sides of the other and the third side of the one greater than the third side of the otlier, tlie angle opposite the greater third...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry - 1876 - 446 pages
...then the angle of one triangle is supplemental to the other. Hence the following property : — 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. A distinction ought to be made between...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876
...a similar set. It may, for instance, be used to prove the converse of (6), namely : — " When two triangles have two sides of the one respectively equal to two sides of the other, but the base of one greater than the base of the other, the vertical angle which is opposite the greater...
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Harvard Examination Papers

Robert Fowler Leighton - 1877 - 343 pages
...GEOMETRY. 1. DEFINE a plane, a parallelogram, a trapezoid, a tangent to a circle. 2. Prove that when two triangles have two sides of the one respectively equal...included angle of the second, the third side of the first is greater than the third side of the second. 3. Show how to draw a tangent to a circle from a point...
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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 the triangle having...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 442 pages
...two spherical triangles have two sides of the one equal respectively to two sides of the other, hut the included angle of the first greater than the included angle of the second, then the third side of the first will be greater than the third side of the second. 3. To draw an •...
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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 sides of...
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Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry - 1868 - 446 pages
...parts alone arc never enough to determine a triangle. 98 UNEQUAL TRIANGLES. 293. Theorem. — When two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the third side in that triangle which has the greater angle, is greater than in the...
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Exercises Contained in Wentworth's Geometry: With Key, Followed by a ...

George Albert Wentworth - 1879 - 196 pages
...two spherical triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first will be greater than the third side of the second. In the spherical...
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Elements of Geometry

George Albert Wentworth - 1881 - 266 pages
...THEOREM. 115. If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first will be greater than the third side of the second. BB В In the А...
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