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" If any side of a triangle be produced, the exterior angle is equal to the sum of the two interior and opposite angles. "
Elements of Plane and Spherical Trigonometry: With Practical Applications - Page 35
by Benjamin Greenleaf - 1862 - 490 pages
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Recent military, naval, and civil service examination papers in mathematics ...

Braithwaite Arnett - 1874
...(1). 1. Draw from a given point a straight line equal to a given straight line. 2. Prove that if a side of a triangle be produced, the exterior angle is equal to the two interior and opposite angles. Trisect a given finite straight line. 3. If a straight line be divided...
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New Elementary Geometry, with Practical Applications

Benjamin Greenleaf - Geometry - 1875 - 204 pages
...equal. 71. Cor. 3. A triangle cannot have more than one angle as great as a right angle. 72. Cor. 4. If any side of a triangle be produced, the exterior...angle is equal to the sum of the two interior and opposite angles. THEOREM XX. Let* ABCDE be any polygon; then the sum of all its interior angles, A,...
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Examination Christmas,1875

Education Department,London - 1876
...Euclid's second corollary to this proposition, and state under what limitation it is true. 1. If a side of a triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of any triangle are equal to two right...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry - 1876 - 446 pages
...a given straight line. Explain what different constructions there are in this proposition. 2. If a 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...
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Annual Report

1876 - 712 pages
...straight lines cut each other show that the opposite vertical angles are equal to each other. 2. If one side of a triangle be produced the exterior angle is equal to the two interior and opposite angles. How many degrees are there in the angle of an equilateral decagon....
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1877 - 458 pages
...two lie in opposite directions, as ABC, DEH. PROPOSITION XXVII. THEOREM. If one side of a triangle is produced, the exterior angle is equal to the sum of the two interior and remote angles ; and the sum of the three interior angles of every triangle is equal to two right anLet...
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Elements of Plane Geometry, Part 1

Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...and DAF are equal, the lines DE and BC are parallel (Prop. XXV.). PROPOSITION XXX.—THEOREM. If one side of a triangle be produced, the exterior angle is equal to the sum of the two interior and opposite angles, and the three angles of the triangle are together equal to two right angles. Let ABC...
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Elements of Geometry and the First Principles of Modern Geometry

Wm. H. H. Phillips - Geometry - 1878 - 236 pages
...R. COR. 5. In an equiangular triangle, each angle is equal to ^ of 2R = | R. XVIII. Theorem. If one side of a triangle be produced, the exterior angle is equal to the two interior angles not adjacent. HYPOTH. In the triangle ABC, one side, AB, is produced, c forming...
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Report of Her Majesty's Civil Service Commissioners: Together ..., Volume 22

1878
...GEOMETRY, ALGEBRA, AND TRIGONOMETRY. Time allowed, 4 hours. [ Tables of Logarithms were supplied."] If a side of a triangle be produced the exterior angle is equal to the two interior and opposite angles, and the three interior angles are together equal to two right angles....
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1879 - 282 pages
...alternate angles EAD, ADC are equal, EF is parallel (I. 25) to BC. Proposition 30. Theorem.—If one side of a triangle be produced, the exterior angle is equal to the two opposite interior angles; and the three interior angles of any triangle are equal to two right...
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