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" Prove that, if two sides of a triangle are unequal, the angle opposite the greater side is greater than the angle opposite the less. "
Elementary Geometry, Plane and Solid: For Use in High Schools and Academies - Page 45
by Thomas Franklin Holgate - 1901 - 440 pages
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1821 - 294 pages
...to one 'another they are acute. PROP. 18, THEOR. In any triangle if one side be greater than another the angle opposite the greater side is greater than the angle opposite the less. Il part cut off with the opposite angle. This connecting line will cut off from the angle opposite...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856 - 168 pages
...the two AB, AC, is greater than the other. But in a triangle having one side greater than another, the angle opposite the greater side is greater than the angle opposite the less ; and in the triangle ABC the angle ABC is greater than ACB ; therefore the angle ABC is opposite the...
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Spherical Trigonometry ...

Isaac Todhunter - Spherical trigonometry - 1859 - 156 pages
...BC; that is, AC is greater than BC. 36. If one side of a spherical triangle be greater than another, the angle opposite the greater side is greater than the angle opposite the other. This follows from the preceding Article by means of the polar triangle. Or thus; suppose the...
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Spherical Trigonometry: For the Use of Colleges and Schools

Isaac Todhunter - Spherical trigonometry - 1863 - 182 pages
...BC; that is, AC is greater than BC. 36. If one side of a spherical triangle be greater than another, the angle opposite the greater side is greater than the angle opposite the other. This follows from the preceding Article by means of the polar triangle. Or thus; suppose the...
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An Elementary Course of Plane Geometry

Richard Wormell - Geometry, Modern - 1868 - 286 pages
...When two angles of a triangle are unequal,Mhe greater side is opposite the greater angle. E 5. When two sides of a triangle are unequal, the angle opposite the greater is greater than that opposite the less. 6. An equilateral triangle is equiangular. 7. An equiangular...
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An Elementary Course of Plane Geometry

Richard Wormell - Geometry, Plane - 1870 - 304 pages
...When two angles of a triangle are unequal, the greater side is opposite the greater angle. 5. When two sides of a triangle are unequal, the angle opposite the greater is greater than that opposite the less. 6. An equilateral triangle is equiangular. 7. An equiangular...
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...one of the two /_s fixed upon. PBOPOSITION XVIII. If one side of a triangle be greater than another, the angle opposite the greater side is greater than the angle opposite the less.* For the construction requisite in this proposition, we must he able, — . 1. From the greater of two...
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National Teachers' Monthly, Volume 2

Education - 1875 - 398 pages
...diagonals of a quadrilateral bisect each other the figure is a parallelogram. 5. PROPOSITION. When two sides of a triangle are unequal, the angle opposite...greater side is greater than the angle opposite the less side. 6. PROPOSITION. A spherical polygon is always within the surface of a hemisphere. 7. PROPOSITION....
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The elementary geometry of the right line and circle

William Alexander Willock - Circle - 1875 - 196 pages
...of Sides respectively Equal, and the Third Side in one is Greater than the third side in the other, the Angle Opposite the greater side is greater than the angle opposite the less. The next subject is that of the Parallelogram, which is a case of two equal triangles reversed on opposite...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 pages
...follow :— THEOREM X. ffypoiftesi's.— ""Wben in a triangle two sides are unequal," Сonclusion — " The angle opposite the greater side is greater than the angle opposite the less." THEOREM XI. (The converse of Theorem X.) Hypothesis. — "When two angles of a triangle are unequal,"...
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