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" If a straight line is drawn through two sides of a triangle parallel to the third side, it divides these sides proportionally. "
A Textbook on Steam Engineering - Σελίδα 6
1902
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - 1829 - 129 σελίδες
...The same might be proved of any number of equal ratios. OF PROPORTIONAL LINES. 70. THEOREM. — If a line be drawn through two sides of a triangle parallel to the third side, it divides those two sides proportionally. More depends upon this proposition than upon any other in...

Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - 1829 - 129 σελίδες
...demonstrate the following proposition, upon which more depends, than upon any other in geometry. — If a line be drawn through two sides of a triangle parallel to the third sidt, it ditides those two sides proportionally — . As the demonstration of this proposition is long,...

Harvard Examination Papers: Collected and Arranged

1873 - 202 σελίδες
...the ratio of two arcs described from their vertices as centres with equal radii. 4. Prove that a line drawn through two sides of a triangle parallel to the third side divides those two sides into proportional parts. 5. State and prove the proportion which exists between...

Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 398 σελίδες
...In like manner we may prove BC = CD, etc. GEOMETRY. — BOOK III. PROPOSITION II. THEOREM. 275. If a line be drawn through two sides of a triangle parallel to the third side, it divides those sides proportionally. Then Fig. 1. " Fig. 2. Ia the triangle ABC let EF be drawn parallel...

Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 398 σελίδες
...sides of equal A). In like manner we may prove B С — CD, etc. 140 PROPOSITION II. THEOREM. 275. If a line be drawn through two sides of a triangle parallel to the third aide, it divides those sides proportionally. A Fig. 1. Kg. 2. In the triangle ABC let EF be drawn parallel...

A Geometry for Beginners

George Anthony Hill - 1880 - 314 σελίδες
...Two other theorems also follow from the preceding investigation : — Theorem II. — If a line is drawn through two sides of a triangle, parallel to the third side, a smaller triangle is formed which is similar to the given triangle. Theorem III. — A line drawn through...

A Geometry for Beginners

George Anthony Hill - 1880 - 314 σελίδες
...parallel to the third side cuts off a smaller" triangle similar to the entire triangle. 11. A line drawn through two sides of a triangle parallel to the third side divides those sides proportionally. 12. I. Law of Similarity. — Two triangles are similar if they...

Elements of Geometry

George Albert Wentworth - 1881 - 250 σελίδες
...like manner we may prove В С = CD, etc. GEOMETRY. — BOOK III. PROPOSITION II. THEOREM. 275. If a line be drawn through two sides of a triangle parallel to the third side, it divides those sides proportionally. A F'g. 1. P1g. 2. In the triangle AB С let EF be drawn parallel...

A Text-book of Geometry

George Albert Wentworth - 1888 - 386 σελίδες
...them when referred to a common unit. PROPORTIONAL LINES. PROPOSITION I. THEOREM. 309. If a line is drawn through two sides of a triangle parallel to the third side, it divides those sides proportionally. Fio. 1. Fia. 2. In the triangle ABC let EF be drawn parallel...

The Elements of Solid Geometry

William C. Bartol - 1893 - 95 σελίδες
...triangles. 360. In a parallelogram the opposite sides are equal and the opposite angles are equal. 361. If a line be drawn through two sides of a triangle parallel to the third side, it divides those sides proportionally. 362. Two triangles which have their sides respectively parallel...




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