5.4 Investigation 1
Triangle Midsegment Properties
Step 1: Draw a triangle on a piece of patty paper. Pinch the patty paper to locate midpoints on the sides. Draw the midsegments. You should now have four small triangles
Step 2: Place a second piece of patty paper over the first and copy one of the four triangles
Step 3: Complete all four triangles by sliding the copy of one small triangle over the other three triangles. Complete your results with the results of your group. Copy and complete the conjecture.
Three Midsegments Conjecture
The three midsegments of a triangle divide it into four congruent triangles
Step 4: Mark all the congruent angles on the original patty paper. If you find it too clustered, redraw the original triangle on regular paper with just one midsegment, as in the diagram at right, and then mark all the congruent angles. Using the corresponding Angles Conjecture or its converse, what conclusion can you make about a midsegment and the large triangle's third side?
The conclusion I can make about the midsegment and the large triangle's third side is that they almost act like parallel lines because if we use the corresponding angles conjecture, we could see they are congruent
Step 5: Complete the length of the midsegment to the large triangle's third side. How do they relate? Copy and complete the conjecture.
Triangle Midsegment Conjecture
A midsegment of a triangle is parallel to the third side and is half the length of the third side