# Qutob Math 1 - Triangle Midsegment Investigation

TRIANGLE MIDSEGMENT INVESTIGATIONS
The midsegment of a triangle is a line segment that connects the midpoint of one side of a triangle to the midpoint of another side. Triangles have 3 midsegments. The midsegments have a number of interesting properties which we will explore in this investigation. See the steps below.

Step 1: Using the triangle underneath "Midsegment Length Investigation", compare the measurements of the midsegments (blue) with the corresponding bases of the triangle (purple). Drag a vertex of the triangle and observe the lengths of the corresponding bases and midsegments How do the measurements of the midsegment and the base compare?
Step 2: Write a TRIANGLE MIDSEGMENT LENGTH CONJECTURE on your paper.
Step 3: Using the triangle underneath "Midsegment Angle Investigation", Compare the measurements of the angles formed by the midsegments (purple) and the 2 sides of the triangle (blue) with the base angles. What types of angles are these? What is the measurement of these angles? Are they congruent? Drag a vertex of the triangle and observe the measures of these angles. Check the boxes for the slopes; what do you notice about the slopes of the 2 segments? If these angles are always congruent, what can we say about the midsegment and the base?
Step 4: Write a TRIANGLE MIDSEGMENT PARALLEL CONJECTURE on your paper