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" The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side. "
A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ... - Page 5
by George Salmon - 1852 - 316 pages
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 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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A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ...

George Salmon - Conic sections - 1852 - 338 pages
...prove that three points are in one right line. Thus the equations a + /3 = 0, /3-y = 0, y + a = 0, interpreted one way, express that two external bisectors...use of these equations of the first degree. Ex. 1. Tfie bisectors of the sides of a triangle meet in a point; viz., in the point a + /3 + y = 0. of the...
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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 - 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...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 142 pages
...therefore 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 plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 286 pages
...given point, and such, that the line joining them shall be parallel to the other given line. 49. A line joining the middle points of two sides of a triangle, is parallel to the base, and equal to the half of it. • I 50. The quadrilateral formed by joining the successive middle...
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Mathematical Questions and Solutions

Mathematics - 1865 - 132 pages
...B + ft cos3 B + y cos C sin2 B) (aa + bft + cy). 3. To find the equation to the circle described on the line joining the middle points of two sides of a triangle. Let D, F (Fig. 3) be the middle points of BC, BA ; join DF and draw the perpendiculars DH, FK. Then...
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Mathematical Questions and Solutions, from the "Educational Times.", Volume 3

1865 - 128 pages
...B + ft cos3 B + 7 cos C sin2 B) (aa + i0 + C7). 3. To find the equation to the circle described on the line joining the middle points of two sides of a triangle. Let D, F (Fig. 3) be the middle points of BC, BA; join DF and draw the perpendiculars DH, FK. Then...
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Mechanics required for the Additional Subjects for Honours at the Previous ...

James McDowell - Mechanics - 1867 - 120 pages
...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 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...
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An Elementary Course of Plane Geometry

Richard Wormell - Geometry, Plane - 1870 - 300 pages
...Therefore 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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