...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...

...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,...

...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...

...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...

...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...

...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...

...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...

...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...

...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...

...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...