1. Definition of a Midsegment:

• A midsegment of a triangle is a line segment that connects the midpoints of two sides of the triangle.
• Each triangle has three midsegments, one for each pair of sides.

2. Properties of the Midsegment:

• Parallelism: The midsegment is parallel to the third side of the triangle (the side not connected by the midsegment).
• Length: The length of the midsegment is half the length of the third side.
  • If the third side is denoted as ( AB ) and the midsegment connects the midpoints of ( AC ) and ( BC ), then ( \text{Midsegment} = \frac{1}{2} \times AB ).
• Divides the Triangle: The midsegment divides the triangle into two smaller triangles, each of which is similar to the original triangle by the Side-Angle-Side (SAS) Similarity Theorem.

3. Triangle Midsegment Theorem:

• This theorem states:
  • A midsegment of a triangle is parallel to one side of the triangle and its length is half the length of that side.
• The theorem can be used to solve problems involving triangle side lengths and parallel lines.

Learn with an example

If TV=48, what is  SW?

SW = ______

Since VW≅UV and ST≅TU,TV is a midsegment of △SUW.

So, TV is half of SW. In other words, SW is twice TV. Set SW equal to twice TV and solve for SW.

SW = 2 . TV

= 2(48) Plug in TV=48

= 96 Multiply

So, SW=96.