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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. "
The Element of Geometry - Page 13
by John Playfair - 1836 - 114 pages
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Introduction and books 1,2

Euclid - Mathematics, Greek - 1908 - 550 pages
...assumption of the uniqueness of the parallel. PROPOSITION 32. In any triangle, if one of the sides be produced, the exterior angle is equal to the two...opposite angles, and the three interior angles of the triangle are equal to two right angles. Let ABC be a triangle, and let one side of it BC be produced...
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Henley's Encyclopędia of Practical Engineering and Allied Trades: A ...

Joseph Gregory Horner - Engineering - 1909 - 560 pages
...each to each, and also the third angle of the one equal to the third angle of the other. (Prop. 26.) If a side of any triangle be produced, the exterior...angles of every triangle are equal to two right angles. (Prop. 32.) Triangles on the same base and between the same parallels are equal to one another. (Prop....
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Annual Report of the Association of Ontario Land Surveyors, Volume 17

Association of Ontario Land Surveyors - Surveying - 1909 - 254 pages
...angles are enual, these straio.ht lines are two and two in the same straio.ht line. 4. If a side of anv triangle be produced, the exterior angle is equal to the two interior and ormosite angles ; and the three interior angles of every triangle are together equal to two right angles....
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Principles of psychology

Herbert Spencer - Philosophy - 1910 - 780 pages
...foregoing theorem is inconveniently long. We shall find a titter one in Proposition xxxii. " If the side of any triangle be produced, the exterior angle...and the three interior angles of every triangle are together equal to two right angles. " Let ABC be a triangle, and let one of its sides BC be produced...
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The Teaching of Geometry

David Eugene Smith - Geometry - 1911 - 360 pages
...is equal to two right angles. Euclid stated this as follows : " In any triangle, if one of the sides be produced, the exterior angle is equal to the two...opposite angles, and the three interior angles of the triangle are equal to two right angles." This states more than is necessary for the basal fact...
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Special Reports on Educational Subjects, Volumes 26-27

Great Britain. Board of Education - Education - 1912 - 1044 pages
...polygons. Measure exterior angle and the two interior and opposite angles of a triangle, and show that the exterior angle is equal to the two interior and opposite angles. Show that the greater angle of a triangle is opposite to the greater side, &c. Third Tear. Arithmetic....
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The Teaching of Mathematics in the United Kingdom

Great Britain. Board of Education - Mathematics - 1912 - 632 pages
...polygons. Measure exterior angle and the two interior and opposite angles of a triangle, and show that the exterior angle is equal to the two interior and opposite angles. Show that the greater angle of a triangle is opposite to the greatei side, &c. Third Year. Simple interest....
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The Teaching of Geometry in Schools: A Report Prepared for the Mathematical ...

Mathematical Association - Geometry - 1923 - 88 pages
...draw a straight line parallel to a given straight line. I. 32 : In any triangle, if one of the sides be produced, the exterior angle is equal to the two...opposite angles, and the three interior angles of the triangle are equal to two right angles. I. 47 : In right-angled triangles the square on the side...
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The Foundations of Geometry and the Non-Euclidean Plane

G.E. Martin - Mathematics - 1997 - 536 pages
...to draw a straight line parallel to a given straight line. 32. In any triangle, if one of the sides be produced, the exterior angle is equal to the two...opposite angles, and the three interior angles of the triangle are equal to two right angles. 33. The straight lines joining equal and parallel straight...
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Annual Report

Saskatchewan. Department of Education - Education - 1910 - 260 pages
...circumstances concurred to give the Midland Dialect predominance ? . GEOMETRY. 1. (a) If a side of a triangle be produced the exterior angle is equal to...opposite angles; and the three interior angles of the triangle are together equal to two right angles. I. 32. (6) Eind the number of right angles in...
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