If the measure of angle ACB is 90°, then which expression represents the value of g? triangle ACB, point E is on segment AC between points A and C and point D is on segment BC between points B and C, creating segment ED, CE equals h, EA equals j, CD equals k, DB equals m, ED equals g, and AB equals f
g equals f over 2
g = 2f
g equals j over h
g equals k over m

The measure of g which is the length of line segment ED is; g = f/2

The image of the triangle is missing and so i have attached it.

From the attached triangle image, we can see that ∠ACB = 90°.

Since ∠ACB = 90°, it means that AB is parallel to ED.

Also, we see that line ED joins the midpoint of AC and CB.

Now, the midpoint theorem of triangles states that; The line segment in a triangle that joins the midpoint of two sides of the triangle is said to be parallel to the third side of that triangle and is also half of the length of the third side.

This means that;

ED = ¹/₂AB

From the attached image, we see that;

ED = g

AB = f

Thus;

g = f/2

Read more about midpoint theorem at; link

Step-by-step explanation:

The picture of the question in the attached figure

In this problem i will assume that point E is the midpoint AC and point D is the midpoint BD

so

we know that

The Triangle Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides, is parallel to the third side and is half the length of the third side

In this problem the segment ED joining two sides of a triangle at the midpoints of those sides

so

ED is parallel to AB and ED is half the length of AB

we have

substitute the given values