| 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... | |
| Dalhousie University - 1891 - 136 pages
...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... | |
| 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,... | |
| Euclid, John Bascombe Lock - Euclid's Elements - 1892 - 188 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... | |
| 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... | |
| George Bruce Halsted - Geometry - 1896 - 208 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... | |
| 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... | |
| Seth Thayer Stewart - Geometry - 1893 - 262 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... | |
| 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... | |
| 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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