University:
High School
Course:
High School Geometry
Academic year:

2020
Views:

168

Pages:

3
Author:

gewektrj

Certainly, here's the analysis of the image you provided: Textual Content: Proportionality Theorems In your own words, write the meaning of each vocabulary term. ratio writing numbers as [a:b] or [\frac{a}{b}] proportion when two ratios are equal [\frac{a_{1}}{b_{1}} = \frac{a_{2}}{b_{2}}] extended proportions when three or more ratios are equal [\frac{a_{1}}{b_{1}} = \frac{a_{2}}{b_{2}} = \frac{a_{3}}{b_{3}} = \frac{a_{4}}{b_{4}}] Theorems Theorem 8.6 Triangle Proportionality Theorem If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally. triangle with a line parallel to one side, dividing the other two sides If [\overline{TU} || \overline{QS}], then [\frac{RT}{TQ} = \frac{RU}{US}] Theorem 8.7 Converse of the Triangle Proportionality Theorem If a line divides two sides of a triangle proportionally, then it is parallel to the third side. triangle with a line dividing two sides If [\frac{RT}{TQ} = \frac{RU}{US}], then [\overline{TU} || \overline{QS}] Theorem 8.8 Three Parallel Lines Theorem If three parallel lines intersect two transversals, then they divide the transversals proportionally. three parallel lines intersecting two transversals [\frac{UW}{WY} = \frac{VX}{XZ}] Theorem 8.9 Triangle Angle Bisector Theorem If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides. triangle with an angle bisector [\frac{AD}{DB} = \frac{CA}{CB}] Extra Practice In Exercises 1 and 2, find the length of AB. Use Triangle Proportions Trick is to write the equation by following the picture triangle with sides labeled 6, 10, and x [\frac{x}{5} = \frac{6}{10}] 10x = 5(6) 10x = 30 x = 3 [\frac{x}{7} = \frac{2}{9}] or [\frac{2}{x} = \frac{9}{7}] 9(x) = 2(7) 9x = 14 x = 14/9 triangle with sides labeled 7, 9, and x In Exercises 3 and 4, determine whether AB || XY If AB || XY then the proportions should be equal triangle with sides labeled 3, 4, 5, and 4 [\frac{3}{4} = \frac{5}{4}] 3/4 ≠ 5/4 So then AB is Not parallel to XY [\frac{6}{7.5} = \frac{5}{4}] or [\frac{4}{7.5} = \frac{5}{6}] 6(5) = 4(7.5) 30 = 30 triangle with sides labeled 7.5, 6, 5, and 4 Same thing So AB || XY