Fg is the midsegment of isosceles abc, and is the midsegment of trapezoid cdef. segments ef, km and dc are parallel. find the measures of segments bc, gf, cd and km. show your work and describe any properties or theorems you use.

BC=60 cm because FG is the midsegment of triangle ABC so it separates the sides of the triangle into two equal segments and 30(2)=60.
GF=22 cm because according to the Triangle Midsegment Theorem, GF=1/2(AC). GF=1/2(44 cm). GF=22 cm. Next, we can conclude EG and DA are 22 cm because the diagram marks them as congruent. So CD=44 cm+22 cm=66 cm. Then, we find that EF=EG+GF=22 cm+22 cm=44 cm. So, using the Trapezoid Midsegment Theorem, we know that KM=1/2(DC+EF). KM=1/2(66 cm+44 cm). KM=1/2(110 cm). KM=55 cm.

Hope this helps and makes sense!

Definitely