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" The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it. "
Elements of Geometry with Exercises for Students: An an Introduction to ... - Page 72
by Aaron Schuyler - 1876 - 372 pages
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Elements of Plane Geometry According to Euclid

Andrew Bell, Robert Simson - Euclid's Elements - 1837 - 290 pages
...of its sides. 9. To bisect a parallelogram by a line drawn from a point in one of its sides. 10. A line joining the middle points of two sides of a triangle, is parallel to the base, and equal to the half of it. 11. The quadrilateral formed by joining the successiYe middle points...
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The Mathematician, Volume 2

1847 - 364 pages
...middle points of the edges AC, AB, BD, BC, DA, DC respectively. Then, since the line drawn to bisect two sides of a triangle is parallel to the third side, and equal to half of it, we have BC = 2KN = 2HG, DC = 2MG = 2LK, AC = 2HL = 2MN, DA = 2KH = 2GN, AB = 2LG = 2KM,...
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A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ...

George Salmon - Curves, Algebraic - 1852 - 338 pages
...triangle meet on the internal bisector of the third angle : interpreted the other way, express that the line joining the middle points of two sides of a triangle is parallel to the third side. 5. We give now some examples of the use of these equations of the first degree. Ex. 1. Tiie bisectors...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 pages
...to four right angles. 10. To describe a square equal to the difference of two given squares. II. A line joining the middle points of two sides of a triangle is parallel to the "base, and equal to half of it. 12. To bisect a given parallelogram by a line drawn from a point in...
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The American Journal of Education and College Review, Volume 2

Education - 1856 - 732 pages
...is an easy deduction, from any one of this series, that a straight line cutting off' equimultiples of two sides of a triangle is parallel to the third side ; and, conversely, a parallel to one side cuts off equimultiples of the other two sides. We need now to have...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858 - 248 pages
...The square of a line is equal to four times the square of its half. 11. The st. line which bisects two sides of a triangle, is parallel to the third side, and equal to one-half of it. 12. If two sides of a triangle be given, its area will be greatest when they contain...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 142 pages
...equidistant from P, and the line BC joining them is parallel to AE. EXERCISE XLIX. — THEOREM. The line joining the middle points of two sides of a triangle is parallel to the base, and equal to the half of it. Let ABC be a triangle, the line DE, that joins the middle points...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...is equal to three times that in the first. VL 119. The line joining the points of bisection of any two sides of a triangle is parallel to the third side, and the triangle so formed is onefourth of the given triangle. 120. If in the triangle ABC, BC be bisected...
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Mechanics required for the Additional Subjects for Honours at the Previous ...

James L. McDowell - Mechanics - 1867 - 120 pages
...through the same point and cut each other in a point of trisection. (EXERCISES, p. 3, No. 5.) Also the straight line joining the middle points of two sides...triangle is parallel to the third side, and equal to half of it. (1) Let AB CD be a rhombus. In the triangles ABC, ADC, the sides AB, AC are equal to AD,...
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An Elementary Course of Plane Geometry

Richard Wormell - Geometry, Plane - 1870 - 304 pages
...DQ=D R. Consequently PR, which is equal to P D+DR, is equal to P D+D Q. Therefore EC=P D+D Q. 2. The line joining the middle points of two sides of a triangle is equal to half the third side, and is parallel to it. Let ABC be the triangle, D and E the middle points...
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