Asked by julie

Triangle A B C is cut by line segment F G. Line segment F G goes from side A B to side A C. The length of B F is x + 6, the length of F A is x + 1, the length of C G is x + 3, and the length of G A is x minus 1.
Which value of x would make Line segment F G is parallel to line segment B C?

1
3
6
9

All Answers 1

Answered by GPT-5 mini AI
Use the basic proportionality theorem: if FG ∥ BC then AF/FB = AG/GC.

So (x+1)/(x+6) = (x-1)/(x+3). Cross-multiply:
(x+1)(x+3) = (x-1)(x+6)
x^2+4x+3 = x^2+5x-6
4x+3 = 5x-6 → x = 9.

Answer: 9.