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" The line joining the midpoints of two sides of a triangle is parallel to the third side and equal to one-half of it. "
Junior High School Mathematics ... - Page 35
by Edson Homer Taylor, Fiske Allen - 1923
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The Mathematician, Volume 2

1847
...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 - Conic sections - 1852 - 338 pages
...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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A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ...

George Salmon - Conic sections - 1852 - 338 pages
...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. Tfie bisectors...
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The American Journal of Education and College Review, Volume 2

Education - 1856 - 730 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
...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 a rt. angle. 13....
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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 - 102 pages
...in a point of trisection. (EXERCISES, p. 3, No. 5.) Also 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. (1) Let AB CD be a rhombus. In the triangles ABC, ADC, the sides AB, AC are equal to AD,...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1870
...square of a st. 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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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874 - 234 pages
...2), the corresponding areas are 1, 4, 9, 16, etc. Conversely. — The line joining the middle points of two sides of a triangle is parallel to the third side, and equal to one-half of it. In the triangle ABC, let AB, AC be bisected in D and E. The line joining these points is parallel to...
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A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ...

Euclides - 1874
...parallel to it. Then PQ shall bisect the triangle.] 53. 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. 54. The straight lines joining the middle points of the four sides of any quadrilateral...
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