Question

Point H is the midpoint of side FK.

Triangles F G H and K J H are connected at point H. The lengths of sides F H and H K are congruent. The lengths of sides G H and J H are congruent. The length of side F G is 3 x minus 2 and the length of corresponding side J K is 2 x + 4.

For the triangles to be congruent by SSS, what must be the value of x?

1
3
6
8

Answer 1

Set the corresponding sides equal: 3x − 2 = 2x + 4.
Solve: x = 6.

(Check: 3(6)−2 = 16 and 2(6)+4 = 16, so the sides match.)