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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 46 INTERCEPTS BY PARALLEL LINES.
Euclid - Page 99
by Euclid, Rupert Deakin - 1903 - 164 pages

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...

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...

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'...

The Poincaré Half-plane: A Gateway to Modern Geometry

Saul Stahl - Geometry, Non-Euclidean - 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 2:1....

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)...

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....

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)...

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....