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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 46 INTERCEPTS BY PARALLEL LINES. "
Euclid - Page 99
by Euclid, Rupert Deakin - 1903 - 164 pages
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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
...middle points of the sides of a triangle perpendicular to the sides meet in a point. 2. The straight Hue which joins the middle points of two sides of a triangle is equal to half the third side. 3. Show how to bisect a triangle by a straight line drawn through one...
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Elementary Synthetic Geometry

George Bruce Halsted - Geometry - 1896 - 210 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 fractional...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1892 - 460 pages
...that is, ZY is par1 to BC. QED [A second proof of this proposition may be derived from i. 38, 39.1 3. The straight line which joins the middle points of two sides of a triangle is equal to half the third side. 4. Shew that the three straight lines which join the middle points of...
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The First Book of Euclid's Elements: Arranged for Beginners

Euclid, John Bascombe Lock - Euclid's Elements - 1892 - 184 pages
...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
...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
...the shortest line which can be drawn from a point to a straight line. 2. The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to one-half of it. 3. Two parallel tangents intercept equal arcs on the circumference of a circle. 4....
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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 - 400 pages
...bisects AC. A line drawn from D to the middle _ point of AC will be parallel to BC. [The line joining the middle points of two sides of a triangle is parallel to the third side.] ( 130.) Then this line will coincide with DE. [But one straight line can be drawn through a given...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 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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