To classify the triangle by its sides, you need to know their lengths. To determine if the triangle is a right triangle, you need to know the slopes of the sides.
Classify by sides: Scalene triangle Right triangle? Yes
Now we can classify the triangle by calculating the side lengths, and then we can determine if it is a right triangle.
Classify by Sides
To classify a triangle by its sides, first we need to calculate the length of the sides using the Distance Formula. Let's start by finding the distance between A( -2, 3) and B( 0, -3). This will give us the value of AB.
We can find the lengths of the other sides in the same way.
Side
Points
sqrt((x_2-x_1)^2+(y_2-y_1)^2)
Length
AB
( -2,3) & ( 0,-3)
sqrt(( 0-( -2))^2+( -3- 3)^2)
2sqrt(10)
AC
( -2,3) & ( 3,-2)
sqrt(( 3-( -2))^2+( -2-( 3))^2)
5sqrt(2)
BC
( 0,-3) & ( 3,-2)
sqrt(( 3- 0)^2+( -2-( -3))^2)
sqrt(10)
As we can see, all the lengths are different. This means △ ABC is scalene.
Right Triangle?
In our diagram, we see that ∠ A and ∠ C are acute angles. In order for △ ABC to be a right triangle, ∠ B must be a right angle. To determine if this is the case, we will first calculate the slope of AB and BC using the Slope Formula.
