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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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Geometry - Plane, Solid and Analytic Problem Solver

Research & Education Association Editors, Ernest Woodward - Mathematics - 2012 - 1080 pages
...product of the lac . . extremes: — - — ** ad - be \bd (2) A line segment which joins the midpoints of two sides of a triangle is parallel to the third side of the triangle, and its length is one-half the length of the third side. (3) If a line is parallel...
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Geometry: A Comprehensive Course

Daniel Pedoe - Mathematics - 1988 - 468 pages
...L', M' and /v" be the midpoints of HA, //Band HC. Using the theorem that the join of the midpoints of two sides of a triangle is parallel to the third side prove that both B'C'M'N' and C'A'N'L' are rectangles, and deduce that A'L', B'M' and C'N' are three...
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Eshbach's Handbook of Engineering Fundamentals

Ovid Wallace Eshbach, Byron D. Tapley - Technology & Engineering - 1990 - 2104 pages
...longest side of a triangle is opposite the largest angle, and vice versa. The line joining the midpoints of two sides of a triangle is parallel to the third side and half its length. If two triangles are mutually equiangular, they are similar, and their corresponding...
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Algebra

T. T. Moh - Mathematics - 1992 - 364 pages
...that V/U is a vector space. | Exercises (1) Use vector space to show that the line passing through the middle points of two sides of a triangle is parallel to the third side. (2) Let Да6с be any triangle. Let us mark down a point b' on the line a6 such that the length ab'...
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The Poincaré Half-plane: A Gateway to Modern Geometry

Saul Stahl - Mathematics - 1993 - 320 pages
...equidistant from a given line consists of two parallel lines. 18. Prove that the line joining the midpoints of two sides of a triangle is parallel to the third side and equal to half its length. 19. Prove that any two medians cut each other into segments whose lengths have ratio...
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Machine Proofs in Geometry: Automated Production of Readable Proofs for ...

Shang-Ching Chou, Xiao-Shan Gao, Jingzhong Zhang - Mathematics - 1994 - 490 pages
...A 6.3 Triangles 6.3.1 Medians and Centroids Example 639 (0.001,1, 2) The line joining the midpoints of two sides of a triangle is parallel to the third side and is equal to one-half its length. We have to prove two results. Constructive description ( (points ABC)...
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Abstract Algebra with Applications: Volume 1: Vector Spaces and Groups

Karlheinz Spindler - Mathematics - 1993 - 780 pages
...called the Main Theorem on Proportions.) (b) Show that the line segment which connects the midpoints of two sides of a triangle is parallel to the third side half as long as the third side. Problem 10. Prove part (c) of Desargues' theorem (1.17). Problem 11....
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Concise Handbook of Mathematics and Physics

Alexander G. Alenitsyn, Eugene I. Butikov, Alexander S. Kondratyev - Science - 1997 - 536 pages
...(starting from the vertex). The middle line of a triangle (that is, the line joining the midpoints of two sides of a triangle) is parallel to the third side and is a half of it (Figure 9. 8c). 9.2.3 Equal triangles Two triangles are called equal (to each other)...
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An Introduction to Mechanics

N. Basu, S. Nanda, P. C. Nayak - Mathematics - 1999 - 438 pages
...and b = b\i + bJ + b3k are collinear. 6. Prove by vector method that the line joining the midpoints of two sides of a triangle is parallel to the third side and is half of the third side. 7. Show that, the internal bisectors of the angles of the triangle are concurrent....
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A Course in Modern Geometries

Judith Cederberg - Mathematics - 2004 - 472 pages
...verify a number of affine properties, including the following. Property la A line joining the midpoints of two sides of a triangle is parallel to the third side. Proof Let M be the midpoint of AB in AABC and let I be the unique parallel to BC through M (see Exercise...
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