...of one equal to an angle of another have the same ratio as the products of the including sides. 3. A line parallel to one side of a triangle divides the other two sides in the same ratio; and conversely. 4. One side of a triangle and either segment cut off by...

...incommensurable case. 6. 2. (a) Prove, by the Pythagorean method aided by simple limit notions, that: A line parallel to one side of a triangle divides the other two sides proportionally. (b) Derive the above proposition from the proposition established in the...

...[Hint: Thru A draw a line parallel to CD, and let the line intersect BC (extended) at E. Then use the theorem: A line parallel to one side of a triangle divides the other two sides proportionally.l AD B The methods used by the Greek mathematicians to construct regular polygons...

...the fourth terms are equal. Thus, ..ace .. a+c+ea if r- = -T = T , then . A t = r- • bdf ' b+d+fb A line parallel to one side of a triangle divides the other two sides proportionally. If a line divides two sides of a triangle proportionally, it is parallel...

...ale = dlb and b/c - dla. Also, c/a - b/d and d/a = b/c.) 8.2 Parallel Lines and Proportions Theorem 1 A line parallel to one side of a triangle divides the other two sides proportionally. A /\ If DE II BC, then / \ AD-AE D / _ \ F BD ~ CE ~/ NT Figure 8.1 e C Theorem...

...largest side, and conversely. S Fig. 11-14. Division of triangle sides into proportional segments 5. A line parallel to one side of a triangle divides the other two sides into proportional segments, and conversely. In Fig. 11-14, if DE is parallel to AC, then...

...Students should also be able to easily complete the construction of ab. The proportion is true because a line parallel to one side of a triangle divides the other two sides proportionally. Solving the proportion for x gives x = ab. Thus, students have constructed...