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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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Rider Papers on Euclid: Books i and Ii, Graduated and Arranged in Order of ...

Rupert Deakin - Euclid's Elements - 1891 - 102 pages
...is divided by each of its medians into two triangles of equal area. 6. The straight line which joins the middle points of two sides of a triangle is parallel to the third side. XXXII. 1. The straight lines drawn through the middle points of the sides of a triangle perpendicular...
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Calendar of Dalhousie College and University

Dalhousie University - 1891
...The lines joining the alternate angles of a regular Hexagon trisect one another. 11. Assuming that the line joining the middle points of two sides of a triangle is equal to half the third side, solve the following : — The base of a triangle is fixed and the sum...
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Plane and Solid Geometry

Seth Thayer Stewart - Geometry, Modern - 1891 - 428 pages
...perpendiculars to it from the other vertices. 4. The straight line joining the points of bisection of two sides of a triangle is parallel to the third side. 5. If a straight line be drawn through any vertex of a parallelogram so as not to intersect the parallelogram,...
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The First Book of Euclid's Elements: Arranged for Beginners

Euclid, John Bascombe Lock - Euclid's Elements - 1892 - 184 pages
...maybe proved that AB, DC are parallel. So that ABCD is a parallelogram. QED Example ii. The straight line joining the middle points of two sides of a triangle is parallel to the base. Let E, F be the middle points of the sides AC, AB of the triangle ABC; it is required to prove...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1892 - 518 pages
...construction; .'. ZX = YC. i 34 Hence AY = YC; that is, AC is bisected at YQED 2. The straight line which joins the middle points of two sides of a triangle, is parallel to the third side. Let ABC be a A , and Z, Y the middle points of the sides AB, AC: then shall ZY be par1 to BC. Produce...
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Elementary Synthetic Geometry

George Bruce Halsted - Geometry - 1896 - 204 pages
...cuts off the same fraction of the other side. 310. Inverse. The sect joining the mid points of any two sides of a triangle is parallel to the third side, and equal to half of it. 311. Corollary. The sect joining points which bound with any vertex of a triangle the same...
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Elementary Geometry

William Chauvenet - 1893 - 340 pages
...Suggestion. Draw DP 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 aides of a triangle...
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Exercises in Stewart's Plane and Solid Geometry: With Solutions for Teachers

Seth Thayer Stewart - Geometry - 1893 - 256 pages
...xx., Cor. i.) ; .-., e = fand а = dif. of _Ls. 4. The straight line joining the points of bisection of two sides of a triangle is parallel to the third side. Through one point of bisection draw a line | to the third side ; it will pass through the other point...
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An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...of a triangle. 2. Prove that any side of a triangle is less than the half-sum of all the sides. 3. The line joining the middle points of two sides of...parallel to the third side and equal to onehalf of it. 4. The two tangents to a circle from an outside point are equal. 5. If two triangles have an angle...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 394 pages
...supplementary, the other two angles are supplementary. MISCELLANEOUS THEOREMS. PRorosiTioN XLVIII. THEOREM. 130. The line joining the middle points of two sides of...parallel to the third side, and equal to one-half of it. Let DE bisect the sides AB and AC of the triangle ABC. To prove DE parallel to BC, and equal to ^BC....
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