To classify the triangle by its sides, you need to know their lengths. To determine if the triangle is a right triangle, we have to know the slope of relevant sides.
Classify by sides: Scalene triangle Right triangle? No
To classify a triangle by its sides means to classify it as either scalene, isosceles, or equilateral. To do that we have to calculate the length of all sides using the Distance Formula. Let's begin by finding the distance between A( 1, 9) and B( 4, 8). This will give us AB.
The length of AB is sqrt(10). We can find the rest of the sides using the same method.
Side
Points
sqrt((x_2-x_1)^2+(y_2-y_1)^2)
Length
AB
A( 1, 9) & B( 4, 8)
sqrt(( 4 - 1)^2 + ( 8 - 9)^2)
sqrt(10)
AC
A( 1, 9) & C( 2, 5)
sqrt(( 2 - 1)^2 + ( 5 - 9)^2)
sqrt(17)
BC
B( 4, 8) & C( 2, 5)
sqrt(( 2 - 4)^2 + ( 5 - 8)^2)
sqrt(13)
As we can see, each side of the triangle has a different length, so △ ABC is a scalene triangle.
Right Triangle?
In our diagram, we see that ∠ A and ∠ C are acute angles. Therefore, if △ ABC is a right triangle, the right angle must be ∠ B. To determine if this is the case, we will first calculate the slope of AB and BC by using the Slope Formula.
Side
Points
y_2-y_1/x_2-x_1
Slope
Simplified Slope
AB
A( 1, 9) & B( 4, 8)
8- 9/4- 1
- 1/3
-1/3
BC
B( 4, 8) & C( 2, 5)
5- 8/2- 4
- 3/- 2
3/2
Since - 13 and 32 are notopposite reciprocals, AB is not perpendicular to BC. Therefore, △ ABC is not a right triangle.
