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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 equal to two right angles. "
Gradations in Euclid : books i. and ii., with an explanatory preface [&c ... - Page 105
by Euclides - 1858
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Annual Report of the Chief Superintendent of Education

1885 - 608 pages
...greater than a second, the angle opposite the first must be greater than that opposite the second. 2. If a side of any triangle be produced the exterior...every triangle are together equal to two right angles. 3. If a parallelogram and a triangle be upon the same base and between the same parallels, the parallelogram...
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University of Oxford. Examination of women. Examination papers

Oxford univ, local exams - 1885 - 358 pages
...with the square on the line between the points of section, is equal to the square on half the line. 5. If a side of any triangle be produced, the exterior...every triangle are together equal to two right angles. Enunciate the first corollary to this proposition. What number of sides must a rectilineal figure have...
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The Practical Teacher, Volume 4

Education - 1885 - 630 pages
...abbreviations for words may be used.] Answer two Questions, including Question 3, if you can. MALES. 1. If a side of any triangle be produced, the exterior angle is Ч1! to the two interior and opposite angles ; and the three interior angles of every triangle...
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Annual Report

Canada. Department of the Interior - 1888 - 756 pages
...perpendicular can be drawn. 6. If one side of a triangle is produced, the exterior angle is equal to the Bum of the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles. 7. Describe a square that shall be equal to a given parallelogram or to...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - Mathematics - 1889 - 354 pages
...method of proof must be geometrical. Great importance will be attached to accuracy.] 1 . If a side of a triangle be produced, the exterior angle is equal to the two interior and opposite angles. Through the vertices of a triangle ABC straight lines, falling within the triangle, are drawn making...
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Practical Surveying: A Text-book for Students Preparing for Examinations Or ...

George William Usill - Surveying - 1889 - 306 pages
...same straight line are parallel to one another. 18. If a side of any triangle B c be produced to D, the exterior angle is equal to the two interior and opposite angles, and the IS three interior angles of every triangle are together equal to two right angles. 19. The exterior...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...congruent (I. 8), and have sides AE, DE parallel respectively to BC, AH (I. 27). PROPOSITION 32. THEOREM. If a side of any triangle be produced, the exterior...triangle are together equal to two right . angles. Let ABC be a A having one side BC produced to D ; then ext. L ACD = twoint. and opp. L s CAB, ABC,...
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Sandhurst Mathematical Papers for Admission Into the Royal Military College ...

Royal Military College, Sandhurst - Mathematics - 1890 - 144 pages
...method of proof must be geometrical. Great importance will be attached to accuracy^ 1. If a side of a triangle be produced, the exterior angle is equal...every triangle are together equal to two right angles. Prove the corollary with regard to the interior angles of any rectilineal figure ; and show from it...
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Practical Plane Geometry: Giving the Simplest Modes of Constructing Figures ...

John Fry Heather - Geometry, Modern - 1890 - 252 pages
...Hence every equilateral triangle is also equiangular, and vice versa. 62. THEOE. 5. If oue side of a triangle be produced, the exterior angle is equal...the two interior and opposite angles ; and the three angles of every triangle are together equal to two right angles (Euc. I. 32). Hence the angles of an...
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Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - Education - 1890 - 530 pages
...and of what proposition may it be regarded as the corollary '! 3. In Prop. 32, Book I., prove that the three interior angles of every triangle are together equal to two right angles, without producing a side of the triangle. 4. If a straight line falling on two other straight lines...
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