On graph paper, graph $\Delta ABC$ if $A(3, 0), B(2, 7)$, and $C(6, 4)$.  

1. What is the most specific name for this triangle? Prove your answer is correct using both slope and side length.

   Hint (a):

   What are the characteristics of the triangle? What kind of triangle has these?

   Remember slope is  $\frac{\Delta y}{\Delta x}$, and for length use the Pythagorean Theorem.

   Answer (a):

   This is an isosceles right triangle because two side lengths are equal and two sides are perpendicular.

2. Find $m\angle A$. Explain how you found your answer.

   Hint (b):

   What trigonometric ratio can you use to find the measure of this angle?
   Refer to the Math Notes Box in Lesson 5.1.2 for the trigonometric ratios and do not forget about inverse trigonometry.