 | Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 272 pages
...of a triangle, parallel to another side, bisects the third side. 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;... | |
 | Charles Hamilton Ashton - Geometry, Analytic - 1902 - 306 pages
...on a line, and find the ratio of their distances from each other. 7410. Show that 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 11. Show that the diagonals of a square or rhombus are perpendicular to each... | |
 | Euclid, Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...pari to BC. QED [A second proof of this proposition may be derived from i. 38, 39.] ', 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... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...A DBF=& ECD, and DF=EC. ButAEDFis&CJ, and DF—AE; hence EC = AE, or AC is bisected at E. COR. — The line which joins the middle points of two sides of a triangle is parallel to the third side, and equal to half of it. For, in the same figure, the line through D \\ to AB passes through E (Th. I.);... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
..."" ' '. ^ .•. 0 is equally distant from AB and BCPROPOSITION XXXIX. THEOREM 238. 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 join the middle points of AB and BC. To Prove DE II to AC, and DE... | |
 | Arthur Schultze - 1901 - 392 pages
...bisects the other non-parallel side. PROPOSITION XXXIX. THEOREM 147. A line which joins the midpoints of two sides of a triangle is parallel to the third side and equal to half of it. BC Hyp. In A ABC: AD = DB, AE = EC. To prove 1°. DE II BC. 2°. DE = \BC. Proof.... | |
 | Linda Bostock, Suzanne Chandler, F. S. Chandler - Juvenile Nonfiction - 1979 - 660 pages
...In Questions 1—8 give proofs based on vector methods. 1) Prove that the line joining the midpoints of two sides of a triangle is parallel to the third side and equal to half of it. 2) Prove that the internal bisectors of the angles of a triangle are concurrent.... | |
 | Howard Whitley Eves - History - 1983 - 292 pages
...FM, EN. Then FE is parallel to BC and equal to one-half of BC (the line segment joining the midpoints of two sides of a triangle is parallel to the third side and is equal to one-half the third side). Similarly, MN is parallel to BC and is equal to one-half of BC. Therefore... | |
 | G.E. Martin - Mathematics - 1997 - 536 pages
...quadrilaterals in absolute geometry are contained in Theorem 22.4. • 22.16 The line through the midpoints of two sides of a triangle is parallel to the third side. 22.17 Theorem 22.17 could have followed Definition 21.9. Why didn't it? Would this rearrangement have... | |
 | Research & Education Association Editors, Ernest Woodward - Mathematics - 2012 - 1080 pages
...product of the lac . . extremes: — - — ** ad - be \bd (2) A line segment which joins the midpoints of two sides of a triangle is parallel to the third side of the triangle, and its length is one-half the length of the third side. (3) If a line is parallel... | |
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The line which joins the middle points of two sides of a triangle is parallel to the third side, and is equal to half the third side. 
