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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. "
Elements of Euclid [selections from book 1-6] adapted to modern methods in ... - Page 68
by Euclides - 1874
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 424 pages
...line parallel to AC. (Sum of A at B = 2 rt. A.) A MISCELLANEOUS THEOREMS. PROP. XLVII. THEOREM. 130. The line joining the middle points of two sides of...parallel to the third side, and equal to one-half of it. Given line DE joining middle points of sides AB and AC, respectively, of A ABC. To Prove DE II BC,...
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The Elements of Plane Geometry

Charles Austin Hobbs - Geometry, Plane - 1899 - 240 pages
...construct a rhomboid when the two diagonals and the included angle are given. Proposition 64. Theorem. 76. The line joining the middle points of two sides of a triangle is parallel to the third side, and is equal to one half the third side. B 57 Conclusion. DE is II to BC, and DE = \ BC. Proof. Draw CF...
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Plane Geometry

William James Milne - Geometry, Modern - 1899 - 258 pages
...two straight lines drawn between the same two points, which by Ax. 12 is impossible. Consequently, the line joining the middle points of two sides of a triangle is parallel to the third side. Proposition XLIII 160. Draw a trapezoid and a line connecting the middle points of the non-parallel...
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Plane and Solid Geometry

William James Milne - Geometry - 1899 - 398 pages
...two straight lines drawn between the same two points, which by Ax. 12 is impossible. Consequently, the line joining the middle points of two sides of a triangle is parallel to the third side. Proposition XLIII 160. Draw a trapezoid and a line connecting the middle points of the non-parallel...
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Plane Geometry

George Albert Wentworth - Geometry, Plane - 1899 - 272 pages
...equal parts on the transversal AC; that is, the line DE bisects AC. 189. COR. 2. The line which joins the middle points of two sides of a triangle is parallel to the third side, and is equal to half the third side. A line drawn through D, the middle point of AB, II to BC, passes through...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 500 pages
...equal parts on the transversal AC; that is, the line DE bisects AC. 189. COR. 2. The line which joins the middle points of two sides of a triangle is parallel to the third side, and is equal to half the third side. A line drawn through D, the middle point of AB, II to BC, passes through...
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1899 - 246 pages
...base of a triangle and bisects one side, it bisects the other side also. 189. The line which joins the middle points of two sides of a triangle is parallel to the third side, and is equal to half the third side. 190. The median of a trapezoid is parallel to the bases, and is equal...
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Pure Mathematics 2

Linda Bostock, Suzanne Chandler, F. S. Chandler - Algebra - 1979 - 660 pages
...In Questions 1—8 give proofs based on vector methods. 1) Prove that the line joining the midpoints of two sides of a triangle is parallel to the third side and equal to half of it. 2) Prove that the internal bisectors of the angles of a triangle are concurrent. 3) Prove...
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Great Moments in Mathematics (before 1650)

Howard Whitley Eves - Mathematics - 1983 - 292 pages
...FM, EN. Then FE is parallel to BC and equal to one-half of BC (the line segment joining the midpoints of two sides of a triangle is parallel to the third side and is equal to one-half the third side). Similarly, MN is parallel to BC and is equal to one-half of BC....
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The Foundations of Geometry and the Non-Euclidean Plane

G.E. Martin - Mathematics - 1997 - 536 pages
...quadrilaterals in absolute geometry are contained in Theorem 22.4. • 22.16 The line through the midpoints of two sides of a triangle is parallel to the third side. 22.17 Theorem 22.17 could have followed Definition 21.9. Why didn't it? Would this rearrangement have...
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