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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 Elements of Plane Geometry ...

Association for the improvement of geometrical teaching - Geometry, Modern - 1884 - 150 pages
...points of the sides of a triangle divide it into four identically equal triangles. *Ex. 59. The straight line joining the middle points of two sides of a triangle is equal to half the base. Ex. 60. If a quadrilateral be formed by joining the middle points of the sides...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884 - 434 pages
...A DBC; which is impossible, since the one is a part of the other. ... AD is || BC. 1. The straight line joining the middle points of two sides of a triangle is || the third side, and = half of it. 2. Hence prove that the straight line joining the middle point...
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Proceedings of the Edinburgh Mathematical Society, Volumes 3-4

Edinburgh Mathematical Society - Mathematics - 1885 - 312 pages
...equivalent to HH, HK, HL, therefore HA is the resultant of HK, HL. Hence, HKAL is a parallelogram ; the line joining the middle points of two sides of a triangle, is parallel to and equal to half of the third side. 3. When P is at S, the centre of the circumscribing circle ABC,...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1885 - 389 pages
...second side, it will bisect the third side ; and, inversely, the sect joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of it. 233. Three or more lines which intersect in the same point are said to be Concurrent. 234....
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The First Six Books of the Elements of Euclid: And Propositions I-XXI of ...

Euclid, John Casey - Euclid's Elements - 1885 - 340 pages
...Exercises. 1. Triangles and parallelograms of equal bases and altitudes are respectively equal. 2. The right line joining the middle points of two sides of a triangle is | arallel to the third ; for the medians from the extremities of the base to these points will each...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...a quadrilateral two of whose angles are right angles. PROPOSITION XLIV. THEOREM. 130. The straight line joining the 'middle points of two sides of a...parallel to the third side and equal to one-half of it. A In the triangle ABC, let B' be the middle point of AB and C" of AC. To prove that B'C' is parallel...
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Elements of Analytic Geometry

George Albert Wentworth - Geometry, Analytic - 1886 - 334 pages
...(7, — 3) ? 52. Prove that the diagonals of a square are perpendicular to each other. 53. Prove that the line joining the middle points of two sides of a triangle is parallel to the third side. 55. Show that the three points (3a, 0), (0, 3b), (a, 2li) are in a straight line. 56. Show that the...
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Elements of Analytic Geometry

George Albert Wentworth - 1886 - 322 pages
...(7, — 3) ? 52. Prove that the diagonals of a square are perpendicular to each other. 53. Prove that the line joining the middle points of two sides of a triangle is parallel to the thh-d side. 5.5. Show that the three points (3a, 0), (0, 3i), (a, 2K) are in a straight line. 56. Show...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1886 - 394 pages
...second side, it will bisect the third side ; and, inversely, the sect joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of it. 233. Three or more lines which intersect in the same point are said to be Concurrent. 234....
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1887 - 331 pages
...Suggestion. Draw DF parallel to AC. See now Proposition VII. and Proposition XXIX. 29. The straight line joining the middle points of two sides of a triangle is parallel to the third side, (v. Exercise 28.) 30. The three straight lines joining the middle points of the sides of a triangle...
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