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" If two sides of a triangle are unequal, the angles opposite are unequal, and the greater angle is opposite the greater side. "
Yale University Entrance Examinations in Mathematics: 1884 to 1898 - Page 35
1898 - 208 pages
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...AC—BC. 93. COROLLARY. An equiangular triangle is also equilateral. PROPOSITION XXVII. THEOREM. 94. If two sides of a triangle are unequal, the angles opposite are unequal, and the greater angle lies opposite the greater side. A B Lay off AD = AB, and join BD. Then in the isosceles triangle ABD,...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 272 pages
...to the base of an isosceles triangle is an axii ' . .*.<.. • w PROPOSITION XXXI. THEOREM. 158. If two sides of a triangle are unequal, the angles...and the greater angle is opposite the greater side. CB In the triangle ACB let AB be greater than AC. To prove ZA GB greater than Z B. Proof. Take AE equal...
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An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...other as the squares of their homologous sides. MASSACHUSETTS INSTITUTE OF TECHNOLOGY, September, 1893. 1. If two sides of a triangle are unequal, the angles opposite are unequal, and the greater angle lies opposite the greater side. 2. State and prove the converse of the preceding. Define a convex polygon;...
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Syllabus of Geometry

George Albert Wentworth - Geometry - 1896 - 68 pages
...are equal, and the triangle is isosceles. 157. Cor. An equiangular triangle is also equilateral. 158. If two sides of a triangle are unequal, the angles...and the greater angle is opposite the greater side. 159. If two angles of a triangle are unequal, the sides opposite are unequal, and the greater side...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...this method correct. Hint. — Apply one of the preceding corollaries. PROPOSITION XIX. THEOREM 76. If two sides of a triangle are unequal, the angles...and the greater angle is opposite the greater side. G1VEN in the triangle ABC the side BC~> side AB. To PROVE the angle m > angle n. On BC take BD = BA,...
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Plane Geometry

George D. Pettee - Geometry, Plane - 1896 - 272 pages
...the Z C; how many degrees are there in each angle ? 32 PLANE GEOMETRY PROPOSITION XVIII 93. Theorem. If two sides of a triangle are unequal, the angles opposite are unequal, the greater angle lying opposite the greater side. Appl. BC>BA. Prove A > C Cons. Make BD = BA. Draw...
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Entrance Examinations in Mathematics, 1884 to 1898 [with Supplements to 1900]

Yale University - 1898 - 212 pages
...volume of the sphere, and compare them with the surface and volume, respectively, of the cube. JUNK 1895. PLANE. 1. If two sides of a triangle are unequal,...centers of all circles whose circumferences pass through t\vo given points. 3. An angle formed by two tangents intersecting without the circumference is measured...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1898 - 266 pages
...vertex to the base of an isosceles triangle is an axis of symmetry. PROPOSITION XXXI. THEOREM. 158. // two sides of a triangle are unequal, the angles opposite...and the greater angle is opposite the greater side. CB In the triangle ACLi let AD fie greater than AC. To prove ZA CB greater than Z B. Proof. Take AE...
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The Essentials of Geometry (plane)

Webster Wells - Geometry - 1898 - 250 pages
...23. How many degrees are there in each angle of an equiangular triangle ? PROP. XXXII. THEOREM. 98. If two sides of a triangle are unequal, the angles opposite are unequal, and the greater angle lies opposite the greater side. A Given, in A ABC, AC > AB. To Prove Z ABC > Z C. Proof. Take AD =...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 500 pages
...of the one equal to the hypotenuse and an acute Z of the other). QED PROPOSITION XXVI. THEOREM. 152. If two sides of a triangle are unequal, the angles...and the greater angle is opposite the greater side. c B In the triangle ACB, let AB be greater than AC. To prove that Z A CB is greater than Z B. Proof....
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