Consider $ΔABC$ with vertices $A(2, 3)$, $B(6, 6)$, and $C(8, –5)$.  

1. Draw $ΔABC$ on graph paper. Is $ΔABC$ a right triangle? Justify your answer.

2. Reflect $ΔABC$ across $\overline{AC}$ to create $ΔA'B'C'$. Find the location of $B'$. What kind of triangle is $∆BB'C$? Justify your answer.

   Step 1(a):

   Compare the slopes of $\overline{AB}$ and $\overline{AC}$. What do you notice?
   What does that tell you about these lines?

   Step 1(b):

   When a figure is reflected what is true about the corresponding angles?
   What about corresponding sides? Specifically how does $∠B$ compare to $∠B'$ and $\overline{BC}$ to $\overline{B'C}$?

   Use the eTool below to help solve the problem.
   Click the link at the right to view full version of the eTool: 7-109 HW eTool