1) Use the MIDPOINT [icon]/images/ggb/toolbar/mode_midpoint.png[/icon] tool to plot the midpoints of any 2 sides of the given triangle. [br]2) Use the SEGMENT [icon]/images/ggb/toolbar/mode_segment.png[/icon] tool to draw the segment (triangle midsegment) connecting these 2 points.[br]3) Use ANOTHER TOOL to illustrate this midsegment (MS) is parallel to the 3rd side of the triangle. [br][br]4) Measure and display the names lengths of the MS and the side of the triangle the MS doesn't touch.[br][br]5) In the algebra view (left side), input [name of MS] / [name of triangle side MS doesn't touch]. [br][br]6) Move [i]A, B[/i], and/or [i]C[/i] around to verify the slopes are equal and the ratio MS / 3rd side = 0.5.
Can you use YET ANOTHER TOOL to prove the midsegment is parallel to the 3rd side of the triangle? [br]Do so.
Yes: Measure a pair of corresponding angles (as done at 1:59 in the screencast) and show that they always remain congruent! [br][br]If a transversal intersects two lines (or segments) so that it forms a pair of congruent corresponding angles, then those lines (or segments) are parallel. [br][br][b]Teachers:[/b][br]Here is one easy, yet powerfully effective means for students to actively discover the Triangle Midsegment Theorem for themselves.
[color=#0000ff]When you're done (or if you're unsure of something), feel free to check by watching the quick silent screencast below the applet. [/color]