17-10-2012, 05:49 PM
The Midpoint Theorem and its Converse
The-Midpoint-Theorem-and-its-Converse.doc (Size: 145.5 KB / Downloads: 193)
The midpoint theorem and its converse.
A. The line which joins the midpoints of two sides of a triangle is parallel to the third side and is equal to half of the length of the third side.
B. The line through the midpoint of one side of a triangle when drawn parallel to a second side bisects the third side.
Proofs
S and T are the midpoints. We have to show ST is parallel to QR
Informal proof
Triangles PST and PQR are similar (SAS)
Angle PST = angle PQR so the lines are parallel