Definition: The triangle midsegment theorem states that a segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long as that side.

Example: In roof truss construction, if UV and VW are midsegments of triangle RST, and RT = 90 inches, then UV = 45 inches, demonstrating the half-length property.

Highlight: The theorem has practical applications in architectural design, particularly in roof truss construction where triangular structures provide strength and stability.

Quote: "Don't forget units" - emphasizing the importance of including proper measurements in calculations.

Definition: A midsegment of a triangle is a segment that connects the midpoints of two sides of the triangle.

Example: In triangle ABC, the midsegments MP, HN, and NP form the midsegment triangle MNP. Using coordinate geometry, we can prove that MN is parallel to JL by showing they have the same slope of 1/4.

Highlight: To prove a segment is a midsegment, you must demonstrate both that it's parallel to the third side and that its length is exactly half of that side.

Vocabulary: The Distance Formula √$x₂-x₁$² + $y₂-y₁$² is used to calculate the length of segments in coordinate geometry.