What can we tell about each of these shapes? We can use slopes to check whether or not quadrilateral  has two pairs of parallel line segments. Sides and each have a slope of . Sides and both have a slope of 6. We can also tell that it does not have any right angles because  and 6 are not opposite reciprocals. So, we can tell that it is a parallelogram but not a rectangle.

Next, we can use the Pythagorean Theorem to see the lengths of each side. The lengths of segments and are units, and the lengths of segments and are units. All side lengths are between 6 and 7 units long, but they are not exactly the same. This means that quadrilateral  is a parallelogram, but not a rhombus or a square.  

Can we find the area of triangle ? That seems tricky, because we don’t know the height of the triangle using as the base. However, angle seems like it could be a right angle. In that case, we could use sides and as the base and height.

To see if is a right angle, we can calculate slopes. The slope of is or , and the slope of is . Since the slopes are opposite reciprocals, the segments are perpendicular, and angle is indeed a right angle. This means that we can think of as the base and as the height. The length of is 10 units, and the length of is 5 units. So the area of triangle is 25 square units because .