1. Midsegments

2. Vocabulary Midsegment – The segment connecting the midpoint of the sides of a triangle, also the segment connecting the legs of a trapezoid

3. Investigation Get your supplies –1 piece of patty paper to be cut in two (1 piece of paper and a marker) –Straight Edge

4. Midsegment Investigation Patty Paper (Regular Paper and marker) Draw a large triangle on a piece of patty paper Fold/Pinch each of the sides to find the midpoint Connect all three midpoints, so you have a triangle drawn with four triangles inside

5. Midsegment Investigation Use a second sheet of patty paper to copy the entire triangle, including the midsegments Compare all four triangles What conclusions can you draw?

6. Midsegment Conjecture The three midsegments of a triangle divide the triangle into four congruent triangles

7. Midsegment Investigation Mark all congruent angles in the triangles. What conclusions can be made about the direction (slope) of the two highlighted lines?

8. Midsegment Investigation Mark all congruent angles in the triangles. What conclusions can be made about the length of the two highlighted lines?

9. Triangle Midsegment Conjecture A midsegment of a triangle is parallel to the third side, and half the length of the third side

10. Practice Problems

16. Trapezoid Midsegment Investigation 2 pieces of patty paper Draw a small trapezoid on the left side of your patty paper. Find the midsegment of the non parallel sides

17. Trapezoid Midsegment Investigation Label the angles 1,2,3 & 4 as shown Copy everything onto the second piece of patty paper

18. Trapezoid Midsegment Investigation Compare angles 1 & 3 and angles 2 & 4

19. Trapezoid Midsegment Investigation On the original drawing, extend the longest base

20. Trapezoid Midsegment Investigation Add the length of the shorter base onto the extended longer base

21. Trapezoid Midsegment Investigation How many times does the midsegment fit onto this extended base (the sum of the two bases)?

22. Trapezoid Midsegment Conjecture The midsegment of a trapezoid is parallel to the bases and equal in length to half the sum of the bases.

23. Trapezoid Midsegment Conjecture If we use software to shrink a base to a point, the trapezoid becomes a triangle. Will the same formula work for the triangle midsegment conjecture?

24. Practice Problems