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: Identify congruent sides

Since \( H \) is the midpoint of \( FK \), \( FH = HK \). For \( \triangle FGH \cong \triangle KJH \) by SSS, \( FG = JK \). So \( 3x - 2 = 2x + 4 \).

Step2: Solve for \( x \)

Subtract \( 2x \) from both sides: \( 3x - 2x - 2 = 2x - 2x + 4 \) → \( x - 2 = 4 \).
Add 2 to both sides: \( x - 2 + 2 = 4 + 2 \) → \( x = 6 \).

Answer:

6