5.1 Midsegments of Triangles • A

midsegment of a triangle

is a segment connecting the midpoints of two sides of the triangle.

– There are two special relationships between a midsegment of a triangle and the third side of the triangle.

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 as long.

Identifying Parallel Segments • What are the three pairs of parallel segments in triangle DEF?

• RS, ST, and TR are the midsegments of triangle DEF.

• Therefore, RS || DF, ST || ED, and TR || FE.

Finding Lengths • In triangle QRS, T, U, and B are midpoints. What are the lengths of segment TU, segment UB, and segment QR?

TU TU

 1 2

SR

 1 (40) 2  20

UB

 1 2

QS

 1 (50) 2

UB

 25

TB

 1 2

QR

30  1 2 (

QR

)

QR

 60

More Practice!!!!!

• Homework – Textbook p. 288 #7 – 24 ALL.