Triangle and Trapezoid Midsegment Investigations
TRIANGLE MIDSEGMENT INVESTIGATION
Step 1
Explore the relationship between the angles of the smaller and larger triangles.
What conclusions can you make about the angles and lengths of the midsegment and the third side of the larger triangle?
Complete conjecture in your notes:
Triangle Midsegment Conjecture
The midsegment of a triangle is __________ to the third side and _____________ the length of the third side.
Step 2
Compare the four triangles created by all three midsegments. What do you notice about their sizes? Complete conjecture in your notes:
Triangle Midsegments Conjecture
The three midsegments of a triangle divide it into ________________.
TRAPEZOID MIDSEGMENT INVESTIGATION
Step 1 Compare the trapezoid’s base angles with the corresponding angles at the midsegment. Are the angles congruent? What can you conclude then about the midsegment compared to the bases? Are your findings about the midsegment true for all trapezoids? Complete the conjecture in your notes.
Trapezoid Midsegment Conjecture
The midsegment of a trapezoid is _________________ to the bases.
Step 2 Let’s investigate how the length of the midsegment of a trapezoid compares to the lengths of the two bases. What do you notice about the length of the midsegment and the sum of the lengths of the two bases? (Note that the Geogebra software rounds each length to the whole number.) Are your findings about the midsegment true for all trapezoids? Complete the conjecture in your notes.
Trapezoid Midsegment Length Conjecture
The length of the midsegment is the average of the lengths of the ____________.