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5.9—Proportions and Similar Triangles Write the following biconditional as a conditional statement and its converse. Then determine whether it is true or false. Two angles are supplementary if and only if they form a linear pair. True or False Conditional:________________________________________________________ __________________________________________________________________ Converse: __________________________________________________________________ __________________________________________________________________ 5.9—Proportions and Similar Triangles calculate Objective: Use proportionality theorems to ____________________ lengths segment ___________________________. Triangle Proportionality Theorem: parallel intersects If a line _____________ to one side of a triangle ______________ the other two sides, then it divides the two sides ________________________. proportionally RT RU If TU || QS , then R TQ US Converse of the Triangle Proportionality Theorem: divides If a line ___________________ two sides of a triangle proportionally, then it is parallel to the __________________ __________________. third side R RT RU Examples: Find the value of each variable. 1. Examples: Find the value of each variable. 2. Examples: Find the value of each variable. 3. Theorem: three parallel lines intersect If ________ ________ transversals, then they two divide ______________ the transversals proportionally. t Z If r || s || t , then UW WY VX XZ Examples: Use the figure to complete the proportion. 1. AB ? CB ? 3. GF ? GE ? 2. CD ? AD ? 4. GF ? ED ? 5. Use the diagram to find LM and MN to the nearest tenth. Theorem: ray bisects an angle of a triangle, then it divides If a ______ the _____________ side into segments whose lengths are opposite proportional to the __________ of the other two sides. lengths AD CA If CD bisects ACB , then DB CB Examples: Find the value of x. 5. Examples: Find the value of x. 6. Examples: Find the value of x. 7.