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" If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles. "
Elements of Geometry and Conic Sections - Page 30
by Elias Loomis - 1857 - 226 pages
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The London University Calendar

London univ - 1846 - 326 pages
...impossible ? 5. If a side of any triangle be produced, show that the exterior angle will be equal to the two interior and opposite angles ; and the three interior angles of every triangle will be equal to two right angles. Also show that all the exterior angles of any rectilineal figure...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 308 pages
...re-entering angles (33), it will be necessary to modify somewhat this method. PROPOSITION XXV. THEOREM. When one side of a triangle is produced, the exterior angle is equal to both the interior and opposits angles taken together. Let the side AB of the triangle ABC be produced,...
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Calendar

University of Cambridge - 1849 - 560 pages
...triangle, the sides of which shall be each equal to twice the base. 2. If a side of any triangle be produced, the exterior angle is equal to the sum of...and the three interior angles of every triangle are together equal to two right angles. Can you give Legendre's method of demonstrating this proposition,...
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The English Journal of Education, Volume 4

Education - 1850
...be parallel to one another. 2. If one side of a triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles. 3. If the square described upon one of the sides of a triangle...
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...re-entering angles (40,) it will be necessary to modify somewhat this method. PROPOSITION xxv. THEOREM. When one side of a triangle is produced, the exterior angle is equal to both the interior and opposite angles taken together. For, conceive BF to be drawn parallel to AC ;...
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A Collection of Problems and Examples, Adapted to the "Elementary Course of ...

Harvey Goodwin - Mathematics - 1851 - 196 pages
...triangle, the sides of which shall be each equal to twice the base. 2. If a side of any triangle be produced, the exterior angle is equal to the sum of...and the three interior angles of every triangle are together equal to two right angles. Can you give Legendre's method of demonstrating this proposition,...
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The First Two Books of the Elements of Euclid ... with Additional Figures ...

Euclides - 1852
...ELEMENTS PROP. XXXII. THEOR. If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles. And the three...interior angles of every triangle are equal to two riffht angles. Let ABC be a triangle, and let one of its sides BC be produced to D; (1.) the exterior...
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Minutes of the Committee of Council on Education

Great Britain. Committee on Education - School buildings - 1855
...a given point without it. 3. If a side of any triangle he produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles. 4. Equal triangles upon the same base and upon the same side of...
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National Society's Monthly Paper

1855
...u given point without it. 3. If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles. 4. Equal triangles upon the same hase and upon the same side of...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...sum of A and C, together with the same angle CBA, is also equal to two right angles (TV, CI) ; hence, the exterior angle is equal to the sum of the two interior and opposite angles. Cor. The exterior angle is greater than either of the interior and opposite angles. OF THE SIDES OF...
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