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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. "
The Elements of Plane Geometry - Side 54
av Charles Austin Hobbs - 1899 - 240 sider
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The First Book of Euclid's Elements: Arranged for Beginners

Euclid, John Bascombe Lock - 1892 - 188 sider
...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 - 1892 - 460 sider
...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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Analytic Geometry for Colleges, Universities, and Technical Schools

Edward West Nichols - 1892 - 300 sider
...the sides opposite meet in a point. 7. Prove that the line joining the middle points of two of the sides of a triangle is parallel to the third side and is equal to one-half of it. 8. The co-ordinates of two of the opposite vertices of a square are (2, 1) and (4,...
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Elementary Synthetic Geometry

George Bruce Halsted - 1896 - 208 sider
...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...
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Elementary Geometry

William Chauvenet - 1893 - 340 sider
...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 - 1893 - 262 sider
...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 - 1894 - 150 sider
...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 two...
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The Elements of Geometry

Webster Wells - 1894 - 394 sider
...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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Elementary Synthetic Geometry of the Point, Line and Circle in the Plane

Nathan Fellowes Dupuis - 1894 - 313 sider
...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 - 1894 - 398 sider
...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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