### Home > CCG > Chapter 6 > Lesson 6.2.5 > Problem6-96

6-96.

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 ✎

1. The triangles share a common angle and parallel lines have congruent corresponding angles, so the triangles are similar by $\text{AA}\sim$.

$\frac{8}{13} = \frac{13}{13 + x}$

$8(13+x)=13·13\\ \ 104+8x=169\\ \qquad \quad 8x=65$

$x=\frac{65}{8}$

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

3.

Vertical angles are equal, so $α=β$.
Parallel lines have equal alternate interior angles, so $θ=γ$.
Triangles are similar by $\text{AA}\sim$.

$6x=8(8)$
$6x=64$
$x\approx10.67$

${\frac{6}{8} = \frac{8}{x}}$