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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. "
Elements of geometry, containing the first two (third and fourth) books of ... - Page 52
by Euclides - 1871
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - Mathematics - 1889
...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 - 272 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 - 515 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 - 132 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, Plane - 1890 - 172 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
...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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Rider Papers on Euclid: Books i and Ii, Graduated and Arranged in Order of ...

Rupert Deakin - Euclid's Elements - 1891 - 79 pages
...one another. 31. To draw a straight line through a given point parallel to a given straight line. 32. If a side of any triangle be produced, the exterior...every triangle are together equal to two right angles. 33. The straight lines which join the extremities of two equal and parallel straight lines towards...
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The Principles of Psychology, Volume 2

Herbert Spencer - Psychology - 1892
...therefore also the angles CBA, BAC, ACB, are together equal to two right angles. "Therefore if aside of any triangle be produced, the exterior angle is...and the three interior angles of every triangle are equal to two right angles. QED" Thus in each step by which the special conclusion IB reached, as well...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1892 - 518 pages
...three interior angles of' a triangle are together equal to two right angles. Let ABC he a triangle, and let one of its sides BC be produced to D : then (i) the exterior angle ACD shall be equal to the sum of the two interior opposite angles CAB, ABC;...
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Entrance Examinations in Mathematics, 1884 to 1898 [with Supplements to 1900]

Yale University - 1898
...DEPARTMENT (YALE COLLEGE) GEOMETRY JUNE 1886. (Four out of five questions are required.) 1. If a side oí any triangle be produced, the exterior angle is equal...every triangle are together equal to two right angles. 2. (Problem) To describe a square on a given straight line. (Show clearly in the figure the methods...
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