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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. "
Essentials of Solid Geometry - Σελίδα 7
των David Eugene Smith - 1924 - 238 σελίδες
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The Mathematician, Τόμος 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...

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

George Salmon - 1852 - 316 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...

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

George Salmon - 1852 - 316 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...

The American Journal of Education and College Review, Τόμος 2

1856
...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
...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...

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

James McDowell - 1867 - 102 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...

Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874
...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...

A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C ...

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...

Euclid simplified, compiled from the most important French works

John Reynell Morell - 1875 - 16 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...

Elements of Geometry with Exercises for Students: An an Introduction to ...

Aaron Schuyler - 1876 - 364 σελίδες
...bisects AC. GEOMETRY.— BOOK I. 104. Corollaries. 1. Tlie straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to its half. (?) 2. The straight line drawn from the middle point of one of the non-parallel...




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