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Describing Triangles

Describing Triangles 1.7 - Solution

arrow_back Return to Describing Triangles

Let's start by drawing the triangle in a coordinate plane.

Classify by Sides

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 and
Evaluate right-hand side
The length of is We can find the rest of the sides using the same method.
Side Points Length

As we can see, and have the same length, so is an isosceles triangle.

Classify by Angles

In our diagram, we see that and are acute angles. We now need to determine what type of angle is. To determine this, we will first calculate the slope of and by using the slope formula.

Side Points Slope Simplified Slope

Looking at the table, we can deduce that is a horizontal segment and is a vertical segment. This means that the intersection of and forms a right angle. Thus, we know that is a right triangle.