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FG is the midsegment of isosceles triangle ABC, and KM is the midsegment of trapezoid CDEF. EF parallel KM parallel DC . Find the following measures. Show your work and describe any properties or theorems you use.

a) BC

b) GF

c) CD

d) KM

(In the picture there is a trapezoid overlapping the triangle, from the top of the triangle to the top of the trapezoid(B to F)its 20mm)and the bottom of the triangle is 30mm))

a) Since FG in halfway down the triangle, BC would be twice BF, and BF is 20.

This makes BC 40.

b) Sing GF is the bottom of the triangle that is half the size of ABC,

GF is 1/2 of AC, so GF is 15.

c) Since AD is the same as GF, and GF was just found as 15, then DA is also 15.

Since DC = DA + AC, DC = 15 + 30 = 45.

d) Since KM is at the midpoint of DEFC, this makes LM halfway between GF and AC. Since GF was 15 and AC was 20, LM is the average between the two, which makes LM 35/2 or 17.5.

Since KL is parallel to DA and KD is parallel to LA, this makes DKLA a parallelogram. That means KL is the same as DA, which is the same as GF, and that is 15.

It can then be said that KM is IL plus LM, which is 7.5 + 15 = 22.5.

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