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" If a line divides two sides of a triangle proportionally, it is parallel to the third side. "
A Text-book of Geometry - Page 136
by George Albert Wentworth - 1888 - 386 pages
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...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...
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Principles of Plane Geometry

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...
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Principles of Plane Geometry

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...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 414 pages
...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 ||...
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Elementary Geometry

William Chauvenet - 1893 - 340 pages
...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...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...determining ratio is 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. 5 1 [Having their sides respectively parallel and...
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Elements of Geometry, Volume 1

Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...determining ratio is 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...
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Syllabus of Geometry

George Albert Wentworth - Mathematics - 1896 - 68 pages
...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...
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Elements of Geometry, Part 1

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...we have AB _AC Ab~^A~c Therefore the line be is parallel to BC. 273 [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. 49 Hence the triangles ABC and Abe, being mutually...
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The Elements of Geometry

Henry W. Keigwin - Geometry - 1897 - 254 pages
...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 to BC. Through R...
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