Geometry 5-4 Midsegments Midsegment of a triangle: a segment that connects the midpoints of two sides of the triangle. Midsegment Triangle: the triangle formed by the 3 midsegments Midpoints: X, Y, Z Midsegments: XY, YZ, ZX Midsegment triangle: ΔXYZ

Midsegment Theorem The midsegment is ½ the length of its parallel side. If BC = 30 DE = 15 A B C E D F BF = FC = 15 If EF = 12 AB = 24 AD = DB = 15

Midsegment Angles All of the angles of the midsegment triangle are the same as the original triangle. A 60° D E 70° 50° C B F

Example Find the perimeter and area of both the original and midsegment triangle. 24 26 10

Example Solve for the value of x given DE and EF are midsegments. A C B F