Question

point h is the midpoint of side fk. for the triangles to be congruent by sss, what must be the value of x? 1 3 6 8

Explanation:

Step1: Use the SSS congruence condition

Since \(H\) is the mid - point of \(FK\), \(FH = HK\). For \(\triangle FGH\cong\triangle KJH\) by SSS (Side - Side - Side), we need \(FG=KJ\).
So, \(3x - 2=2x + 4\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides of the equation \(3x - 2=2x + 4\):
\(3x-2x-2=2x - 2x+4\), which simplifies to \(x - 2=4\).
Then add \(2\) to both sides: \(x-2 + 2=4+2\).

Answer:

\(x = 6\), so the answer is \(6\).