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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. "
The College Euclid: Comprising the First Six and the Parts of the Eleventh ... - Page 310
by Euclides - 1865
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Minutes of the Committee of Council on Education

Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...straight line of an unlimited length, from a given point without it. 3. If a side of any triangle he produced, the exterior angle is equal to the two interior...every triangle are together equal to two right angles. 4. Equal triangles upon the same base and upon the same side of it, are between the same parallels....
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Geometry - 1855 - 334 pages
...EAF is drawn through the given point A parallel to the given straight line BC. PROP. XXXII. THEOR. If a side of any triangle be produced, the exterior angle is equal to the tivo interior and opposite angles ; and the three interior angles of tvery triangle are equal to two...
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Manual of Method for the use of teachers in elementary schools

W F. Richards - Elementary school teaching - 1856 - 198 pages
...opposite to equal sides, show that these two triangles are not necessarily equal to one another. 4. If a side of any triangle be produced, the exterior...every triangle are together equal to two right angles. 5. If a straight line be divided into any two parts, the square of the whole line is equal to the squares...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856 - 252 pages
...into two equal angles. 2. Any two sides of a triangle are together greater than the third side. 4. If a side of any triangle be produced, the exterior...and the three interior angles of every triangle are equal to two right angles. If two sides of any triangle be produced, the two exterior angles are together...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856 - 168 pages
...together equal to the two FBC, DBC, that is. to two right angles. XIV.— EUCLID I. 32. If one 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. Let ABC (Fig. 9) be a triangle, and...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Euclid's Elements - 1856 - 346 pages
...given point A parallel to the given straight line BC. PROP. XXXII. THEOR. If a side of any triangle oe produced, the exterior angle is equal to the two interior and opposite angles ; andlthe three interior angles of every triangle are equal to two right i Let ABC be a triangle, and...
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Considerations on the Suggestions of the University Commissioners with ...

Henry Latham - 1857 - 390 pages
...Construct a triangle of which the base, the sum of the other sides, and the vertical angle are given. 2. If a side of any triangle be produced, the exterior...every triangle are together equal to two right angles. At what angles are the sides of a regular duodecagon inclined to each other? 3. If a straight line...
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The Pupil-teacher: A Monthly Journal of Practical Educational ..., Volume 3

1857 - 400 pages
...sides of a triangle, parallel to the base; and prove that the line so drawn bisects the other side. 5. If a side of any triangle be produced, the exterior...is equal to the two interior and opposite angles. If the triangle is equilateral, what is the relation between the exterior angle and the adjacent interior...
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The English Journal of Education, Volumes 11-13

Education - 1857 - 1266 pages
...EUCLID. FIRST YEAR. SECTION I. — 1. The angles at the base of an isosceles triangle arc equal. 2. The three interior angles of every triangle are together equal to two right angles. 3. To a given straight line apply a rectangle equal to a given rectilineal figure. SECTION II. —...
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Parliamentary Papers, Volume 25

Great Britain. Parliament. House of Commons - Bills, Legislative - 1858 - 694 pages
...less than the other two sides of the triangle, but shall contain a greater angle. 3. PKOP. XXXII.— If a side of any triangle be produced, the exterior...every triangle are together equal to two right angles. 4. Enunciate and prove the corollaries of the last proposition. 5. PROP. XLIV. — To a given straight...
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