Objective: To use the properties of midsegments to solve problems. Chapter 5 Lesson 1 Objective: To use the properties of midsegments to solve problems.

Midsegment In ∆ABC above,     is a triangle midsegment. A midsegment of a triangle is a segment connecting the midpoints of two sides.

Theorem 5-1 Triangle Midsegment Theorem If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side, and is half its length.

Example 1: Finding Lengths In ∆EFG, H, J, and K are midpoints. Find HJ, JK, and FG. HJ = ½ EG HJ = ½ (100) HJ = 50 HK = ½ FG 40 = ½ FG JK = ½ FE 80 = FG JK = ½ (60) JK = 30

Example 2: Finding Lengths AB = 10 and CD = 18. Find EB, BC, and AC. EB = ½ DC EB = ½ (18) EB = 9 BC=AB AC=AB+BC BC=10 AC=10+10 AC=20

Example 3: Identifying Parallel Segments In ∆DEF, A, B, and C are midpoints. Name pairs of parallel segments. AC EF BC ED AB DF

Assignment Page 246 #1-19