Section 6.6: Using Proportionality Theorems Chapter 6: Similarity Section 6.6: Using Proportionality Theorems

Section 6.6: Using Proportionality Theorems 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. In ΔQRS, if TU || QS, then R T U Q S

Section 6.6: Using Proportionality Theorems Find the value of the variable: 1. 2. Q K 36 y x 10 U L R 14 22 M P S 20 N 10 T

Section 6.6: Using Proportionality Theorems Converse of the Triangle Proportionality Theorem: If a line divides two sides of a triangle proportionally, then it is parallel to the third side In ΔQRS, if , then TU || QS R T U Q S

Section 6.6: Using Proportionality Theorems Given the diagram, determine whether CD is parallel to EF. B 72 96 C 30 E D 40 F

Section 6.6: Using Proportionality Theorems Midsegment of a triangle: a segment that connects the midpoints of two sides of a triangle The Midsegment Theorem: The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long. If ΔABC, if CD = DA and CE = EB, then DE || AB and DE = ½ AB C D E A B

Section 6.6: Using Proportionality Theorems Find the length of UY Find the value of the variable U Y 17 V X W p 16

Section 6.6: Using Proportionality Theorems Theorem: If three parallel lines intersect two transversals, then they divide the transversals proportionally. Y W U V X Z

Section 6.6: Using Proportionality Theorems Using the information in the diagram, find the distance between First Street and Main Street 160 m 320 m 1 2 340 m 3 First Street Main St Second St

Section 6.6: Using Proportionality Theorems 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. A C D B

Section 6.6: Using Proportionality Theorems In the diagram, <ABD ≅ <CBD. Use the given side lengths to find the length of DC. B 32 24 A D C 40

Section 6.6: Using Proportionality Theorems Homework: Pg. 400 #3-17 (all)