 | William Chauvenet - Geometry - 1871 - 380 pages
...should then have AB = A'B', BC=B'C', etc. PROPOSITION II.— THEOREM. 19. Conversely, if a straight line divides two sides of a triangle proportionally, it is parallel to the third side. Let DE divide the sides AB, AC, of the triangle ABC, proportionally; then, DE is parallel... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...should then have AB = A'B', BC=B'C', etc. PROPOSITION II.— THEOREM. 19. Conversely, if a straight line divides two sides of a triangle proportionally, it is parallel to the third side. Let DE divide the sides AB, AC, of the triangle ABC, proportionally; then, DE is parallel... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...|| ad. To BE PROVED. OA : Oa = OB : O& = OC : Oc = OD : Od. xvni. Theorem. Converse!y, if a straight line divides two sides of a triangle proportionally, it is parallel to the third side. HYPOTH. In the triangle ABC, AD : DB=AE : EC. To BE PROVED. The line DE [| BC. \ BOOK III.]... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...: : CF : FH. In like manner, EG : GB :: FH : HD; and so on. PROPOSITION XVI. THEOREM. // a straight line divides two sides of a triangle proportionally, it is parallel to the third side. Let ABC be a triangle, and let DE divide AB and AC, so that AD : DB :: AE : EC; then DE... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...to the base of a triangle .divides the other two sides proportionally. PROPOSITION II. If a straight line divides two sides of a triangle proportionally, it is parallel to the third side. PROPOSITION III. Two triangles are similar when they are mutually equiangular. PROPOSITION... | |
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...makes equal angles with AB and AC : prove that Proposition 1 3. Theorem. 301. Conversely, if a straight line divides two sides of a triangle proportionally, it is parallel to the third side. Hyp. Let DE cut AB, AC in the A ABC so that 7^ = -r=. To prove DE || to BC. Proof. If DE... | |
 | William Chauvenet - 1893 - 340 pages
...AD : DB = AE : EC (». 10), and also that PROPOSITION II.—THEOREM. 15. Conversely, if a straight line divides two sides of a triangle proportionally, it is parallel to the third side. Let DE divide the sides AB, AC, of the triangle ABC, proportionally; then DE is parallel... | |
 | George Clinton Shutts - Geometry - 1894 - 412 pages
...either of its segments as the other side is to its corresponding segment. AB AC AB AC L o prove = or = . AD AE DB EC tion in the conclusion of the proposition,...proportionally, it is parallel to the base. A Let А В С be a triangle, and let D £ divide the sides, so AD AE that DB = EC' To prove that DE is parallel... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 416 pages
...of the segments of one side equals the ratio of the segments of the other side. PROPOSITION XIV. If a line divides two sides of a triangle proportionally, it is parallel to the base. PROPOSITION XV. Two triangles which are mutually equiangular are similar. PROPOSITION XVI. If two triangles... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...are cut by any number of parallels, the corresponding intercepts are proportional. 312. If a straight line divides two sides of a triangle proportionally, it is parallel to the third side. 313. The bisector of an angle of a triangle divides the opposite side into segments proportional... | |
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If a line divides two sides of a triangle proportionally, it is parallel to the third side. 
