 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...If two lines 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 to... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...their ratio of similitude. AB is parallel to A'B', BC to B'C', etc. § 273 [If a straight line divide two sides of a triangle proportionally, it is parallel to the third side.] Hence angle ABC=A'B'C', angle BCD = B'C'D', etc. § 51 [Having their sides respectively parallel and... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 376 pages
...C' in the given proportion, we have AB _AC Ab ~ Ac ' Therefore the line be is parallel to BC. § 260 [If a straight line divides two sides of a triangle...proportionally, it is parallel to the third side.] And the angle Abc = the angle B, and Acb—C. § 48 Hence the triangles ABC and Abe, being mutually equiangular,... | |
 | Joseph Johnston Hardy - Geometry, Analytic - 1897 - 398 pages
...through two sides of a triangle parallel to the third side, it divides those sides proportionally. 24. If a straight line divides two sides of a triangle proportionally, it is parallel to the third side. 25. If two triangles have their sides respectively parallel, or respectively perpendicular, they are... | |
 | Henry W. Keigwin - Geometry - 1897 - 254 pages
...given ratio. 11. In Fig. 101 draw KJ parallel to AB ; then prove PROPOSITION II. THEOREM. 235. If a line divides two sides of a triangle proportionally, it is parallel to the third side. In the triangle ABC let PR divide the sides AB, AC proportionally. It is to be proved that PR is parallel... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...COR. By composition (204), AD + DB: AD = AE + EC: AE, or AB:AD = AC:AE. EXERCISES. Q A 1. Conversely, if a straight line divides / \ two sides of a triangle...proportionally, it is parallel to the third side. by any number of parallels, AC, EF, GH, j \ 2. If two straight lines AB, CD are cut EI __ \ F BD, the... | |
 | George Albert Wentworth - Geometry - 1898 - 462 pages
...GK= HB : KD. If the two lines AB and CD were parallel, the correspondPROPOSITION II. THEOREM. 312. If a straight line divides two sides of a triangle proportionally, it is parallel to the third side. •0 In the triangle ABC let EF be drawn so that 9 AB = AC AE AF To prove EF II to B O. Proof. From... | |
 | George Albert Wentworth - Geometry - 1898 - 266 pages
...corresponding intercepts would be equal, and the above proportion be true. PROPOSITION II. THEOREM. >312. // a straight line divides two sides of a triangle proportionally, it is parallel to the third side. In the triangle ABC let EF be drawn so that AI3 = AC AE AF To prove EF \\toBC. Proof. From E draw EH... | |
 | Henry W. Keigwin - Geometry - 1898 - 250 pages
...parallel to AB ; then prove AC-.AK:: BC :: UK. 1 PROPOSITION II. THEOREM. 235. If a line divides twn sides of a triangle proportionally, it is parallel to the third side. In the triangle ABO let PR divide the sides AB, AC proportionally. It is to be proved that PR is parallel... | |
 | George Albert Wentworth - Geometry - 1899 - 496 pages
...MN = KD. § 180 Now AH : AM = AF : AL = FH : LM = HB : MN. § 343 BND PROPOSITION XIV. THEOREM. 345. If a straight line divides two sides of a triangle proportionally, it is parallel to the third side In the triangle ABC, let EF be drawn so that AB^AC AE ~ AF' To prove that EF is II to BC. Proof. From... | |
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If a line divides two sides of a triangle proportionally, it is parallel to the third side. 
