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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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Hungarian Problem Book III

György Hajós, Andy Liu, G. Neukomm, János Surányi - Mathematics - 2001 - 164 pages
...the other side that is also part of the locus. Midpoint Theorem. The segment joining the midpoints of two sides of a triangle is parallel to the third side and equal to half its length. Proof. Let E and F be the respective midpoints of the sides CA and AB of an arbitrary...
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Calculus: Concepts and Methods

Ken Binmore, Joan Davies - Business & Economics - 2001 - 574 pages
...to prove the following elementary geometrical results: (i)* The line segment joining the midpoints of two sides of a triangle is parallel to the third side and equal to half of it. (ii) If one pair of opposite sides of a quadrilateral is parallel and equal. then so also...
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Math for All Learners: Geometry

Pam Meader, Judy Storer - Mathematics - 2001 - 108 pages
...sides of a triangle using a compass. • discover that a segment whose endpoints are 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. Overview Through construction...
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Mathematical Computing: An Introduction to Programming Using Maple®

David Betounes, Mylan Redfern - Computers - 2001 - 430 pages
...proves, usmg vector methods, the well-known geometric fact: the line segment joining the midpoints of two sides of a triangle is parallel to the third side and half as long. Example 6.3 (Altitudes of a Triangle) Le: points ABC be the vertices of a triangle in...
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Connections Maths 10: Stage 5.2/5.1

Ajit Kalra, James Stamell - Mathematics - 2006 - 540 pages
...AB = ED, prove that С is the midpoint of AE. в Prove that the interval joining the midpoints of 2 sides of a triangle is parallel to the third side and equal to half its length. 14 ABC is an isosceles triangle in which AB = AC. BMand CNare drawn perpendicular...
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Euclidean Geometry and Transformations

Clayton W. Dodge - Mathematics - 2004 - 310 pages
...of Menelaus' theorem, the following theorems are given. 4.4 Theorem The line joining the midpoints of two sides of a triangle is parallel to the third side. Let M and N be the midpoints of sides AB and CA of triangle ABC. (See Fig. 4.4.) Let line MN meet side...
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A Textbook of Engineering Mathematics: For B.Sc. (Engg.). B.E., B.Tech., M.E ...

N. P. Bali, N. Ch. Narayana Iyengar - Engineering mathematics - 2004 - 1438 pages
...vectors represented by the other sides. (Punjab, 1986 S) 2. Prove that the line joining the mid-points of two sides of a triangle is parallel to the third side and half of it. (N. Bengal, 1989 ; Marathwada, 1990) 3. Prove that the lines joining the mid-points of...
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Vector Analysis

K. A. Stroud, Dexter J. Booth - Mathematics - 2005 - 366 pages
...QB-QB = 0 QB + QD = 0 Here is one more. Example 4 Prove by vectors that the line joining the mid-points of two sides of a triangle is parallel to the third side and half its length. Let D and E by the mid-points of AB and AC respectively. We have DE = M + ÄE Now...
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New Sat Rea: The Very Best Coaching & Study Course

Mel Friedman, Lina Miceli, Robert Bell, Michael Lee, Sally Wood, Adel Arshaghi, Suzanne Coffield, Michael McIrvin, Anita Price Davis, Research & Education Association, George DeLuca, Joseph Fili, Marilyn Gilbert, Bernice E. Goldberg, Leonard Kenner - Study Aids - 2005 - 886 pages
...the slope of BC. Denote it by m. 4-0 _ 1 10 + 6~4 m We know that a segment that joins the midpoints of two sides of a triangle is parallel to the third side. So, DE is parallel to BC, and as a result they have the same slope. Therefore, the slope of DE is -...
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CDS (Combined Defence Service Exam)

E.S.Ramasamy - 2006 - 838 pages
...triangle are equal then the angles opposite to them will also be equal. 4. The line joining the mid points of two sides of a triangle is parallel to the third side. 5. The angle opposite to the greater side is always greater than the angle opposite to the smaller...
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