Definition: A [b]midsegment of a triangle[/b] is a segment that connects the midpoints of any 2 sides of that triangle. [br]Question: [b]How many midsegments does a triangle have? [/b][br][br]Let's proceed:[br][br]In the applet below, [b]points [color=#1551b5]D[/color] and [color=#c51414]E[/color] are midpoints of 2 sides of triangle ABC.[/b] One [color=#0a971e]midsegment[/color] of Triangle ABC is shown in [color=#0a971e]green[/color]. [br]Move the vertices A, B, and C of Triangle ABC around. As you do, observe the values given off to the right side. [br]Then, answer the questions below the applet.
1) What do you notice about the slopes of segments [color=#0a971e]DE[/color] and AB? What does this imply about these 2 segments? [br][br][br]2) What does the ratio of [color=#0a971e]DE[/color] to AB tell us about the [color=#0a971e]midsegment [/color]of any triangle? [br][br][br]3) If we refer to the black side of the triangle as the triangle's "3rd side", write two observations that you made between the midsegment and the third side. Be sure to use the phrase "3rd side" in each blank below. [br][br] [b]The [color=#0a971e]MIDSEGMENT of a triangle[/color] is ALWAYS [br][br] i) ________________________________________________________________________, and[br][br] ii) ________________________________________________________________________. [/b]