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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

## 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...

## 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...

## 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...

## 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 ||...

## 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...

## 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...

## 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...

## 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...