 | George Salmon - Conic sections - 1852 - 329 pages
...triangle meet on the internal bisector of the third angle : interpreted the other way, express that the line joining the middle points of two sides of a triangle is parallel to the third side. 5. We give now some examples of the use of these equations of the first... | |
 | George Salmon - Conic sections - 1852 - 338 pages
...triangle meet on the internal bisector of the third angle : interpreted the other way, express that the line joining the middle points of two sides of a triangle is parallel to the third side. 5. We give now some examples of the use of these equations of the first... | |
 | Euclides - 1860 - 142 pages
...therefore equidistant from P, and the line BC joining them is parallel to AE. EXERCISE XLIX. — THEOREM. The line joining the middle points of two sides of a triangle is parallel to the base, and equal to the half of it. Let ABC be a triangle, the line DE, that joins... | |
 | Mathematics - 1865 - 132 pages
...equation becomes afty + bya + caft = (a cos A sin2 B + ft cos3 B + y cos C sin2 B) (aa + bft + cy). 3. To find the equation to the circle described on...; join DF and draw the perpendiculars DH, FK. Then q- = BF . BH = $ ca cos B ; r2 = CD . CK = CD {CD + DF cos C} = ^a(a + 6cosC) ; p2=AH. AF=£c(c + 6... | |
 | Richard Wormell - Geometry, Plane - 1870 - 304 pages
...Therefore DQ=D R. Consequently PR, which is equal to P D+DR, is equal to P D+D Q. Therefore EC=P D+D Q. 2. The line joining the middle points of two sides of a triangle is equal to half the third side, and is parallel to it. Let ABC be the triangle, D and E the middle... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...1, 2, 3, 4, etc. (I. App., schol. 2), the corresponding areas are 1, 4, 9, 16, etc. Conversely. — 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. In the triangle ABC, let AB, AC be bisected... | |
 | Richard Wormell - 1876 - 268 pages
...through the middle point of a side of a triangle parallel to the base it will bisect the other side. 43. The line joining the middle points of two sides of a triangle is equal to half the third side and is parallel to it. 44. If from points in the base of an isosceles... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...the position of a straight line, it follows, that if AD = DB, and AE = EC, then DE || BC ; that is, the line joining the middle points of two sides of a triangle is parallel to the third D/. side. COR. 2, Since DE = BF = FC, DE = ^ that is, the line joining the... | |
 | Euclides - 1883 - 176 pages
...Analysis. — Suppose DEF to be the triangle required. It is a well-known proposition (Ex. 100) that the line joining the middle points of two sides of a triangle is || to the third side ; .-. AC is || DF, BC || DE, and AB || EF. Synthesis. — The construction... | |
 | Richard Wormell - Geometry, Plane - 1883 - 210 pages
...¿ED A, and ¿ D С F — ¿ DAE. Сonsequently triangles ADE, С DF are equal, and AD = С D. 43. The line joining the middle points of two sides of a triangle is equal to Jialf the third side, and is parallel to it. Let AB С be the triangle, D and E the middle... | |
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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. 
