 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...DF : EG. BD = CE, DF = EG, whence AB = AC; hence, the above proportion is still true. v THEOREM II. If a straight line divides two sides of a triangle proportionally, it will be parallel to the third side. In the triangle ABC, let DE divide AB and AC so that AD : DB ::... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...C.), AE : EG : : 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 is parallel... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...I. A parallel 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 IV. Two... | |
 | George Albert Wentworth - Geometry - 1888 - 272 pages
...: MN. That is, AF : CG = FH: GK= HB -. KD. PROPOSITION II. THEOREM. 312. // a straight line divide 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 EF II to BC. Proof. From E draw... | |
 | James Wallace MacDonald - Geometry - 1889 - 80 pages
...segments. See Book II., Proposition VI. Proposition XVII. A Theorem. 142. If a straight line divide the sides of a triangle proportionally, it is parallel to the third side. Proposition XVIII. A Problem. 143. To divide a given line into parts proportional to given lines, or... | |
 | James Wallace MacDonald - Geometry - 1894 - 76 pages
...segments. See Book II., Proposition VI. Proposition XVII. A Theorem. 142. If a straight line divide the sides of a triangle proportionally, it is parallel to the third side. Proposition XVIII. A Problem. 143. To divide a given line into parts proportional to given lines, or... | |
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...respectively, and it 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 is not ||... | |
 | William Chauvenet - 1893 - 340 pages
...I. A parallel 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 IV. Two... | |
 | George Clinton Shutts - Geometry - 1894 - 412 pages
...theory of proportion the former can be deduced from the latter. PROPOSITION XV. 292. Theorem. // a line divides two sides of a triangle 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... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...these angles are proportional. L A' GIVEN—in the triangles ABC and A'B'C', the angle A=A' and AR AC Place the triangle A'B'C' on ABC so that the angle...divides two sides of a triangle proportionally, it is par allel to the third side.] and the angles b and c are equal respectively to B and C. § 49 Hence... | |
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If a line divides two sides of a triangle proportionally, it is parallel to the third side. 
