5.4 Investigation 2
Trapezoid Midsegment Properties
Step 1: Draw a small trapezoid on the left side of a piece of patty paper. Pinch the paper to locate the midpoints of the nonparallel sides. Draw the midsegment.
Step 2: Label the angles as shown. Place a second piece of patty paper over the first and copy the trapezoid and it's midsegment.
Step 3: Compare the trapezoid's base angles with the corresponding angles at the midsegment by sliding the copy up over the original.
Step 4: Are the corresponding angles congruent? What can you conclude about the midsegment and the bases? Compare your results with the results of other students.
Yes the corresponding angles are congruent and I can conclude that the midsegment and the bases act almost like parallel lines with the corresponding angles being congruent.
The midsegment of a triangle is half the length of the third side. How does the length of the midsegment of a trapezoid compare to the lengths of the two bases? Let's investigate.
Step 5: On the original trapezoid, extend the longer base to the right by at least the length of the shortest base
Step 6: Slide the second patty paper under the first. Show the sum of the lengths of the two bases by marking a point on the extension of the longer base.
Step 7: How many times does the midsegment fit onto the segment representing the sum of the length of the two bases? What do you notice about the length of the midsegment and the sum of the lengths of the two bases?
A midsegment fits twice onto the segment representing the sum of the length of the two bases. I noticed the length of the midsegment is half the sum of the length of the two bases.
Step 8: Combine your conclusions from step 4 and 7 and complete this conjecture.
Trapezoid Midsegment Conjecture
The midsegment of a trapezoid is parallel to the bases and is equal in length to the average of both bases