Question

point h is the midpoint of side fk for the triangles to be congruent by sss, what must be the value of x? 3x - 2 2x + 4 1 3 6 8

Explanation:

Step1: Use the SSS congruence condition

Since \(H\) is the mid - point of \(FK\), \(FH = HK\). Also, for \(\triangle FGH\) and \(\triangle KJH\) to be congruent by SSS (Side - Side - Side), \(FG=KJ\).

Step2: Set up the equation

We are given \(FG = 3x - 2\) and \(KJ=2x + 4\). Set \(3x - 2=2x + 4\).

Step3: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(3x-2x-2=2x - 2x+4\), which gives \(x - 2=4\).
Add \(2\) to both sides: \(x-2 + 2=4 + 2\). So \(x = 6\).

Answer:

\(6\)