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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. "
Plane Geometry - Σελίδα 78
των Fletcher Durell - 1904 - 372 σελίδες
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The Mathematician, Τόμος 2

1847 - 364 σελίδες
...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...

A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ...

George Salmon - 1852 - 338 σελίδες
...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...

A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ...

George Salmon - 1852 - 338 σελίδες
...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...

The American Journal of Education and College Review, Τόμος 2

1856 - 732 σελίδες
...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...

Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858 - 248 σελίδες
...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...

Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 σελίδες
...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...

Mechanics required for the Additional Subjects for Honours at the Previous ...

James McDowell - 1867 - 120 σελίδες
...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...

A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ...

Euclides - 1874 - 120 σελίδες
...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...

Elements of Euclid Adapted to Modern Methods in Geometry

Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 236 σελίδες
...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...

Euclid simplified. Compiled from the most important French works, approved ...

John Reynell Morell - 1875 - 220 σελίδες
...corresponding height are given. EXERCISES ON BOOK III. 92. The straight line which joins the centres of two sides of a triangle is parallel to the third side, and equal to half that side. 93. The straight lines which join the centres of the consecutive sides of...




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