 | Euclides, James Hamblin Smith - 1879 - 376 pages
...but AD is || to BF, .: AD is || to BF. QED Ex. 1. The straight line, joining the points of bisection of two sides of a triangle, is parallel to the base, and is equal to half the base. PROPOSITION XLI. THEOREM. If a parallelogram and a triangle be upnn the... | |
 | Charles Scott Venable - 1881 - 380 pages
...the corresponding side of the given triangle. 25. (Corollary of 24. ) The straight line which joins the middle points of two sides of a triangle is parallel to the third side and equal to the half of it. And, conversely, if, through the middle point, D, of the side,... | |
 | 1882 - 486 pages
...equal to AN. That is, AC is bisected in N. NOTE. — MN is equal to half of AB. Hence the straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to its half, Draw MP,LR, parallel to AF, and join ML, PR. Then from the property... | |
 | Mathematical association - 1883 - 86 pages
...triangle parallel to the base passes through the middle point of the other side. COR. 3. The straight line joining the middle points of two sides of a triangle is parallel to the base. [Cor. 2. and Rule of Identity.] SECTION 4. PROBLEMS. PROB. 1. To bisect a given angle. PROB. 3. To... | |
 | 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 suggested... | |
 | 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... | |
 | Euclides - 1884 - 214 pages
...triangles into which a parallelogram is divided by its diagonals, are equal in area. (154) The straight line joining the middle points of two sides of a triangle is parallel to the other side. (155) The straight lines which join the middle points of the three sides of a triangle,... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 242 pages
...line AB, erect a perpendicular BD equal to the side of the given square. Complete. See Prob. IX. 13. A line joining the middle points of two sides of a triangle is parallel to the third, and equal to the half of it. 14. Bisect the sides of a quadrilateral, join the points of bisection,... | |
 | Euclides - 1884 - 182 pages
...BEC are equal ; show that AH and CD are parallel. 3. The straight line which joins the middle Jpoints of two sides of a triangle is parallel to the base and equal to half of it. 4. Straight lines which join the middle points of adjacent sides of a quadrilateral form... | |
 | Association for the improvement of geometrical teaching - Geometry, Modern - 1884 - 150 pages
...points of the sides of a triangle divide it into four identically equal triangles. *Ex. 59. The straight line joining the middle points of two sides of a triangle is equal to half the base. Ex. 60. If a quadrilateral be formed by joining the middle points of the sides... | |
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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. 
