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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. "
Theoretical Geometry: Based on the Various Geometry Books by Godfrey and Siddons - Page 46
by Arthur Warry Siddons, Reginald Thomas Hughes - 1926 - 173 pages
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Elements of Plane Geometry According to Euclid

Andrew Bell - 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, BD = 2HM =...
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A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ...

George Salmon - Conic sections - 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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Elements of geometry and mensuration

Thomas Lund - Geometry - 1854 - 522 pages
...(12) Shew that, if any two sides of a triangle be bisected, the line joining the points of bisection is parallel to the third side, and equal to half of it. (13) Define similar triangles ; can triangles be similar and not equal? Can they be equal and not similar?...
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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 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...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, AC each to...
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