Line LM is the midsegment of trapezoid ABCD. If AB =50 and DC = 135, what is LM? Please show all work in order to receive full credit for this problem
In a trapezoid, a midsegment is a line that connects the midpoints of the two non-parallel sides.
First, we need to find the length of side AD, which is equal to the length of side BC. Since AB is parallel to DC, we can use the Midsegment Theorem to find the length of LM.
The Midsegment Theorem states that the length of the midsegment is equal to the average of the lengths of the two parallel sides.
So, to find the length of side AD, we take the average of AB and CD:
AD = (AB + CD) / 2
AD = (50 + 135) / 2
AD = 185 / 2
AD = 92.5
Now, we know that LM is equal to half the length of AD.
LM = AD / 2
LM = 92.5 / 2
LM = 46.25
Therefore, the length of LM is 46.25.