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" In an isosceles triangle, the angles opposite the equal sides are equal. "
Elements of Geometry: With Practical Applications to Mensuration - Page 19
by Benjamin Greenleaf - 1863 - 320 pages
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Annual Register of the United States Naval Academy, Annapolis, Md, Volumes 25-32

United States Naval Academy - 1874 - 888 pages
...all the angles of a polygon of n sides. If the polygon is regular, what is each angle Î Prove that in an isosceles triangle the angles opposite the equal sides are equal. 2. Prove that the straight Hues which bisect two adjacent supplementary angles are perpendicular to...
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New Elementary Geometry, with Practical Applications

Benjamin Greenleaf - Geometry - 1875 - 204 pages
...side BA equal to ED, the side CA equal to FD, and the angle A equal to the angle D. THEOREM VI. 46. In an isosceles triangle, the angles opposite the...sides are equal. Let ABC be an isosceles triangle, in A which the side AB is equal to the side AC; then will the angle B be equal to the angle C. Conceive...
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Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 376 pages
...the triangles are equal in all their parts, (P. 8), which was to be proved. PROPOSITION XII. THEOREM. In an isosceles triangle the angles opposite the equal sides are equal. Let ACD be an isosceles triangle in which D CD is equal to DA. Let the base AC be bisected in E and from...
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Elements of Geometry with Exercises for Students: An an Introduction to ...

Aaron Schuyler - Geometry - 1876 - 384 pages
...AD (56, 2). But B and C are opposite the equal sides, AC, AB, of the isosceles triangle ABC. Hence, in an isosceles triangle, the angles opposite the equal sides are equal. 60. Corollaries. 1. The line bisecting the vertical angle of an isosceles triangle bisects the base...
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Euclid, book i., propositions i. to xxvi., with exercises and alternative ...

Euclides - 1877 - 58 pages
...to each other; and if the equal sides be produced, the angles on the other side of the base shall be equal. Let ABC be an isosceles triangle in which the side AB is equal to the side AC, and let the sides AB, AC be produced to D and E ; then the angle ABC shall be equal to the angle ACB,...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 436 pages
...respectively to an homologous side and acute angle of the other. TRIANGLES. PROPOSITION XXVIII. THEOREM. 2. In an isosceles triangle the angles opposite the equal sides are equal. Let ABC be ал isosceles triangle, having tue sides AC and С B equal. ч We are to prove Z. A = ZB From С draw...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...respectively to an homologous side and acute angle of the other. TRIANGLES. PROPOSITION XXVIII. THEOREM. 112. In an isosceles triangle the angles opposite the equal sides are equal. Let A Л С be ал isosceles triangle, having the sides A С and С B equal. We are to prove ZB From С...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...respectively tcr an homologous side and acute angle of the other. TRIANGLES. PROPOSITION XXVIII. THEOREM. 112. In an isosceles triangle the angles opposite the equal sides are equal. С Let ABС be an isosceles triangle, having the sides A С and С B equal. We are to prove A = ZB...
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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...intersection E. Therefore the two triangles coincide, and are equal in all respects. THEOREM XII. 82. In an isosceles triangle the angles opposite the equal sides are equal. In the isosceles triangle ABC let AB and BC be the equal sides ; then the angle A is equal to the angle...
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Cornell University Register and Catalogue

Cornell University - 1880 - 868 pages
...tangent to a circle, the projection of one straight line upon another, four proportional magnitudes. 2. In an isosceles triangle the angles opposite the equal sides are equal to each other. Every equilateral triangle is also equiangular. An isosceles triangle is symmetric about...
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