To classify the triangle by its sides, you need to know their lengths. To determine if the triangle is a right triangle, you have to know the slope of relevant sides.
Classification by sides: Isosceles triangle Right triangle? Yes
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 length between A( 2, 3) and B( 6, 3).
The length of AB is 4. 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( 2, 3) & B( 6, 3)
sqrt(( 6 - 2)^2 + ( 3 - 3)^2)
4
AC
A( 2, 3) & C( 2, 7)
sqrt(( 2 - 2)^2 + ( 7 - 3)^2)
4
BC
B( 6, 3) & C( 2, 7)
sqrt(( 2 - 6)^2 + ( 7 - 3)^2)
4sqrt(2)
As we can see, AB and AC have the same length, so △ ABC is an isosceles triangle.
Right Triangle?
In our diagram, we see that ∠ B and ∠ C are acute angles. Therefore, if △ ABC is a right triangle, the right angle must be ∠ A. To determine if this is the case, we will first calculate the slope of AB and AC by using the Slope Formula.
Side
Points
y_2-y_1/x_2-x_1
Slope
Simplified Slope
AB
A( 2, 3) & B( 6, 3)
3- 3/6- 2
0/4
0
AC
A( 2, 3) & C( 2, 7)
7- 3/2- 2
4/0
Undefined
Looking at the table, we can deduce that AB is a horizontal segment and AC is a vertical segment. This means that the intersection of AB and AC forms a right angle. Therefore, △ ABC is in fact a right triangle.
