Over Lesson 7–3 Complete the proportion. Suppose DE=15, find x. Suppose DE=15, find EG. Find the value of y. FE Ch 9.5  D F G E H x 28 DG = FH DE ?   1214 y y + 3

Ch 9.5 Proportional Parts Standard 7.0 Students use theorems involving the properties of parallel lines cut by a transversal. Learning Target: I will be able to use proportions to determine whether lines are parallel to sides of triangles. Ch 9.5

Vocabulary midsegment of a triangle A segment of a triangle is called a midsegment when its endpoints are the midpoints of two sides of the triangle. Ch 9.5 A BC Midpoint of AB Midpoint of AC

Concept Ch 9.5 Theorem 9-6

Example 2 Determine if Lines are Parallel In order to show that we must show that Ch 9.5 Since the sides are proportional. Answer: Since the segments have proportional lengths, GH || FE.

Example 2 A.yes B.no C.cannot be determined Ch 9.5

Concept Ch 9.5 Theorem 9-7

Example 3 Use the Triangle Midsegment Theorem A. In the figure, DE and EF are midsegments of ΔABC. Find AB. Ch 9.5 ED = AB Triangle Midsegment Theorem __ 1 2 5= AB Substitution __ = AB Multiply each side by 2. Answer: AB = 10

Example 3 Use the Triangle Midsegment Theorem B. In the figure, DE and EF are midsegments of ΔABC. Find FE. Ch 9.5 FE = (18) Substitution __ FE = BC Triangle Midsegment Theorem FE = 9 Simplify. Answer: FE = 9

Example 3 Use the Triangle Midsegment Theorem C. In the figure, DE and EF are midsegments of ΔABC. Find m  AFE. Ch 9.5  AFE  FEDAlternate Interior Angles Theorem m  AFE =m  FEDDefinition of congruence m  AFE =87Substitution By the Triangle Midsegment Theorem, AB || ED. Answer: m  AFE = 87

Example 3 A.8 B.15 C.16 D.30 A. In the figure, DE and DF are midsegments of ΔABC. Find BC. Ch 9.5

Example 3 B. In the figure, DE and DF are midsegments of ΔABC. Find DE. A.7.5 B.8 C.15 D.16 Ch 9.5

Example 3 C. In the figure, DE and DF are midsegments of ΔABC. Find m  AFD. A.48 B.58 C.110 D.122 Ch 9.5