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" The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side. "
A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ... - Page 5
by George Salmon - 1852 - 316 pages
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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 Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1892 - 460 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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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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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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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 a triangle is 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...
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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 a triangle is 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...
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Elementary Synthetic Geometry of the Point, Line and Circle in the Plane

Nathan Fellowes Dupuis - Geometry - 1894 - 313 pages
...one side of a triangle, parallel to a second side, bisects the third side. And, 2, the line through the middle points of two sides of a triangle is parallel to the third side. 85. Theorem. — The three medians of a triangle pass through a common point. CF and AD are medians...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 398 pages
...is parallel to AD and BC. II. To prove EF = \ (AD + BC). Since EG bisects AB and BD, EG = %AD. (1) [The line joining the middle points of two sides of a triangle is equal to one-half the third side.] • ( 130.) And since GF bisects BD and CD, GF= ^BC. (2) Adding...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...through the vertex, th. 27 or cor. 1 proves it. Draw the figure. 3. The line joining the mid-points of two sides of a triangle is parallel to the third side. For if not, suppose through the mid-point of one of those sides a line is drawn parallel to the base...
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