### Home > GC > Chapter 6 > Lesson 6.2.5 > Problem 6-84

6-84.

For each part below, decide if the triangles are similar. If they are similar, use their similarity to solve for

*x*. If they are not similar, explain why not. Homework Help ✎

Parallel lines have equal corresponding angles, so *θ = α*.

By shared angles, *β = β*.

By AA~, the triangles are similar.

12*x* = 4(8+*x*)

12*x* = 32 + 4*x*

8*x* = 32 *x* = 4

Is there enough information to prove that the triangles are similar?

Use the same method as for part (a).

Vertical angles are equal, so *α = β*.

Parallel lines have equal alternate interior angles,

so *θ = γ*.

Triangles are similar by AA~.

6*x* = 8(8)

6*x* = 64

*x* ≈ 10.6