The triangle in the figure has vertices at points P(0, 0), Q(0, 6.5), and R(3, 2).  Classify the triangle by its angles

To classify the triangle by its angles, we need to calculate the slopes of the lines formed by the sides of the triangle. The slope of a line is given by the formula (y2 - y1) / (x2 - x1).

1. Calculate the slope of PQ: The coordinates of P are (0,0) and the coordinates of Q are (0,6.5). The slope of PQ is (6.5 - 0) / (0 - 0) = undefined. This means PQ is a vertical line.

2. Calculate the slope of QR: The coordinates of Q are (0,6.5) and the coordinates of R are (3,2). The slope of QR is (2 - 6.5) / (3 - 0) = -4.5 / 3 = -1.5.

3. Calculate the slope of RP: The coordinates of R are (3,2) and the coordinates of P are (0,0). The slope of RP is (0 - 2) / (0 - 3) = 2 / 3.

Now, we know that if two lines are perpendicular, the product of their slopes is -1. In this case, the product of the slopes of PQ (undefined) and QR (-1.5) is not -1, the product of the slopes of QR (-1.5) and RP (2/3) is not -1, and the product of the slopes of RP (2/3) and PQ (undefined) is not -1. Therefore, the triangle does not have a right angle.

Since all the angles in the triangle are less than 90 degrees, the triangle is an acute triangle.