Fg is the midsegment of isosceles abc , and km is the midsegment of trapezoid cdef . ef km dc || || , bf=20mm, ac=30mm. find the following measures. show your work and describe any properties or theorems you use. (a) bc (b) gf (c) cd (d) km

Part A:

Given that FG is the midsegment of isosceles triangle ABC, by the triangle midsegment theorem, we have that BF = FC and AG = GB.

Thus, BC = BF + FC = 2BF (since BF = FC)

Therefore, the measure of side BC is 2(20 mm) = 40 mm

Part B:

Similarly by the triangle midsegment theoren, GF = 1/2AC.

Given that the measure of side AC is 30 mm, therefore, the measure of side GF is 1/2(30 mm) = 15 mm

Part C:

From the given figure, EG = GF = AD.

Since, we obtained from part B that the measure of side GF is 15 mm, thus EG = GF = AD = 15 mm.

CD = CA + AD = 30 mm + 15 mm = 45 mm

Therefore, the measure of side CD is 45 mm.

Part D:

Given that EF is parallel to KM is parallel to DC, BA is a transversal such that EG = DA, this implies that line DE is parallel to line AG.

Since, line DE is parallel to line AG and KM is the midsegment of trapezoid CDEF, this implies that line KL is parallel to line DE is parallel to line AG. And ADEG forms a parallelogram with KL as the midsegment. This means that EG = KL = DA = 15 mm.

Also, LM is halfway between GF and AC, and thus the measure of line LM is the average of the measures of line GF and AC.

Thus, LM = (15 mm + 30 mm) / 2 = 45 mm / 2 = 22.5 mm

Therefore, the measure of line KM = The measure of line KL plus the measure of line LM = 15 mm + 22.5 mm = 37.5 mm

and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

.

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .