Line JK is the median of triangle GIJ.If GK=10x-4,IK=5x+6, find the measure of live IG
To find the measure of line IG in triangle GIJ, we first need to understand what it means for line JK to be the median. In a triangle, the median is a line segment that connects a vertex to the midpoint of the opposite side. In this case, line JK connects vertex G to the midpoint of side IJ.
Since line JK is the median, it divides side IJ into two congruent segments. This means that GK is equal to IK. Therefore, we can set up the equation:
GK = IK
10x - 4 = 5x + 6
To find x, we need to isolate it on one side of the equation. Let's start by subtracting 5x from both sides:
10x - 5x - 4 = 5x - 5x + 6
5x - 4 = 6
Then, let's add 4 to both sides to isolate the term with x:
5x - 4 + 4 = 6 + 4
5x = 10
Finally, divide both sides by 5 to solve for x:
5x/5 = 10/5
x = 2
Now that we know the value of x, we can substitute it back into the expressions for GK and IK to find their respective lengths. Let's start with GK:
GK = 10x - 4
GK = 10(2) - 4
GK = 20 - 4
GK = 16
Next, let's find IK:
IK = 5x + 6
IK = 5(2) + 6
IK = 10 + 6
IK = 16
Since GK = IK = 16, we can conclude that line IG also has a length of 16 in triangle GIJ.