| 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 - 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... | |
| 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... | |
| 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 - 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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