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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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Solid Geometry

Charles Austin Hobbs - Geometry, Solid - 1921 - 216 pages
...triangle parallel to the third side,'it divides the two sides proportionally. Prop. 76. // a line divides two sides of a triangle proportionally, it is parallel to the third side. Prop. 79. Two triangles are similar when they are mutually equiangular. Prop. 79, Cor. I. Two triangles...
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Bulletin, Issues 25-53

United States. Office of Education - 1921 - 1286 pages
...a triangle parallel to the third side, it divides these sides proportionally. (6) If a line divides two sides of a triangle proportionally, it is parallel to the third side. (Proofs for commensurable cases only.) (c) The segments cut off on two transversals by a series of...
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The Reorganization of Mathematics in Secondary Education

National Committee on Mathematical Requirements - Mathematics - 1922 - 84 pages
...a triangle parallel to the third side, it divides these sides proportionally. (b) If a line divides two sides of a triangle proportionally, it is parallel to the third side. (Proofs for commensurable cases only.) (c) The segments cut off on two transversals by a series of...
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The Reorganization of Mathematics in Secondary Education: A Report of the ...

National Committee on Mathematical Requirements - Mathematics - 1923 - 680 pages
...a triangle parallel to the third side it divides these sides proportionally. (b) If a line divides two sides of a triangle proportionally it is parallel to the third side. (Proofs for commensurable cases only.) (f) The segments cut off on two transversals by a series of...
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Junior High School Mathematics: 1st-3d Book, Book 3, Part 2

Edson Homer Taylor, Fiske Allen - Mathematics - 1923 - 104 pages
...corresponding segment. Prove this, using Theorems XL III and XL IV. THEOREM XLV 191. // a line divides two sides of a triangle proportionally it is parallel to the third side. Given A ABC having line PQ cutting AB at P and p> r> f>f) BC at Q, so that To prove PQ || AC. Proof....
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...807. In a given line, AB, to find a point, C, so that PROPOSITION XVI. THEOREM 300. If a line divides two sides of a triangle proportionally, it is parallel to the third side. Given in A AEC, AB : BC = AD: DM. To prove DB parallel to EC. Proof. Through C, draw CE' parallel to...
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The Teaching of Mathematics in the Elementary and the Secondary School

Jacob William Albert Young - Mathematics - 1924 - 484 pages
...a triangle parallel to the third side it divides these sides proportionally. (b) If a line divides two sides of a triangle proportionally it is parallel to the third side. (Proofs for commensurable cases only.) (c) The segments cut off on two transversals by a series of...
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A Geometry Reader

Julius J. H. Hayn - Geometry, Plane - 1925 - 328 pages
...L, PARALLEL FROM PROPORTIONAL SEGMENTS 195 Proposition XII. Theorem 202. // a straight line divides two sides of a triangle proportionally, it is parallel to the third side. Hyp.: Given the triangle ABC with EF so placed that CE : EA = CF : FB. Det. : To prove that EF is parallel...
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Mathematics: Course of Study for Senior and Junior High Schools

Baltimore (Md.). Department of Education - Mathematics - 1924 - 182 pages
...it divides those sides proportionally. Proof for the commensurable case only. b. If a line divides two sides of a triangle proportionally, it is parallel to the third side. c. The segments cut off on two transversals by a series of parallels are proportional. d. The bisector...
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The Reorganization of Mathematics in Secondary Education (part I): A ..., Part 1

National Committee on Mathematical Requirements - Mathematics - 1927 - 208 pages
...triangle parallel to the third side it divides these sides proportionally. [57, cd] (b) If a line divides two sides of a triangle proportionally it is parallel to the third side. (Proofs for commensurable cases only.) [58*, cd*] (c) The segments cut off on two transversals by a...
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