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" ... greater than the included angle of the second, then the third side of the first is greater than the third side of the second. "
Elements of Plane and Solid Geometry - Page 50
by George Albert Wentworth - 1877 - 398 pages
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A System of Popular Geometry: Containing in a Few Lessons So Much of the ...

George Darley - Euclid's Elements - 1836 - 172 pages
...that is, greater than the side DF. This, &c. [See NOTE Q.] ART. 45. If two triangles have two sides of the one equal respectively to two sides of the other, but their bases unequal,—the vertical angle of that triangle which has the greater base is greater than...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...THEOREM XXI. If two triangles have two sides of the one respectively equal to two sides of the other, and the included angle of the first greater than the included angle of the second, the third side of the first will be greater than the third side of the second. FIRST BOOK. In the two...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 468 pages
...XXI. If two triangles have two sides of the one respectively equal to two sides of the other, and, the included, angle of the first greater than the included angle of the second, th'> third side of the first will be greater than the third side of the second. In the two triangles...
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An Elementary Course of Plane Geometry

Richard Wormell - Geometry, Modern - 1868 - 286 pages
...the triangles are unequal (fig. 79). When two triangles have two sides of the one respectively equal to two sides of the other, but the included angle of the one greater than the included angle of the other, the base of that which has the greater angle is greater...
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Harvard Examination Papers

Robert Fowler Leighton - 1877 - 343 pages
...that when two triangles have two sides of the one respectively equal to two sides of the other and the included angle of the first greater than the 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...
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Exercises Contained in Wentworth's Geometry: With Key, Followed by a ...

George Albert Wentworth - 1879 - 196 pages
...AB .f AC. Ex. 2. On the same sphere, or on equal spheres, if two spherical triangles have two sides of the one equal respectively to two sides of the...will be greater than the third side of the second. In the spherical A ABC and A'B'C, let AB = A'B',AC = AC,ZA>ŁA'; then is BC> B'C. If the parts are...
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Elements of Geometry

George Albert Wentworth - 1881 - 266 pages
...equiangular triangle is also equilateral. PROPOSITION XXXI. THEOREM. 115. If two triangles have two sides of the one equal respectively to two sides of the...will be greater than the third side of the second. BB В In the А ABC and ABE, let AB = AB, BC — BЕ; but żABO ż ABE. We are to prove A С > A E....
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Elements of Geometry

George Albert Wentworth - Geometry, Plane - 1882 - 268 pages
...also equilateral. GEOMETRY. BOOK I. PROPOSITION XXXI. THEOREM. 115. If two triangles have two sides of the one equal respectively to two sides of the...the second, then the third side of the first will be (/realer than the third side of the second. EE In the А AB С and ABE, let AB = AB, B С = BE; but...
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Essentials of Geometry

Alfred Hix Welsh - Geometry - 1883 - 326 pages
...Therefore, if two triangles have two sides of the one equal to two sides of the other, each to each, but the included angle of the first greater than the included angle of the second, the third side of the first will be greater than the third side of the second. QUERIES. 1. What is...
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Report of the School Committee of the City of Providence, Presented to the ...

Public schools - 1884 - 630 pages
...equivalent to the sum of the squares on the other two sides. 7. Prove that if two triangles have two sides of the one equal respectively to two sides of the...angle of the second, then the third side of the first is greater than the third side of the second. 8. Prove that if the middle points of the three sides...
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