# Triangles

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### Identifying Scalene, Isosceles, and Equilateral Triangles

Triangles are classified according to the length of their sides or the measure of their angles. These classifications come in threes, just like the sides and angles themselves.

### Using The Triangle Inequality Principle

The triangle inequality principle states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This idea comes up in a fair number of problems, so

### Identifying Triangles by Their Angles

You can classify triangles by their angles as well as by their sides. The classifications based on angles are as follows:

### Finding the Altitude of a Triangle

The altitude of a triangle is a segment from a vertex of the triangle to the opposite side (or to the extension of the opposite side if necessary) that’s perpendicular to the opposite side; the opposite

### Working with Pythagorean Triple Triangles

The first four Pythagorean triple triangles are the favorites of geometry problem-makers. These triples — especially the first and second in the list that follows — pop up all over the place in geometry

### How to Find the Incenter, Circumcenter, and Orthocenter of a Triangle

Every triangle has three “centers” — an incenter, a circumcenter, and an orthocenter — that are located at the intersection of rays, lines, and segments associated with the triangle:

### Identifying the 45 – 45 – 90 Degree Triangle

A 45 – 45 – 90 degree triangle (or isosceles right triangle) is a triangle with angles of 45°, 45°, and 90° and sides in the ratio of

### Identifying the 30 – 60 – 90 Degree Triangle

The 30 – 60 – 90 degree triangle is in the shape of half an equilateral triangle, cut straight down the middle along its altitude. It has angles of 30°, 60°, and 90° and sides in the ratio of

### Determining a Triangle's Area from Its Base and Height

If you know the base and height of a triangle, you can use a tried-and-true formula to find its area. You likely first ran into the basic triangle area formula in about sixth or seventh grade. If you’ve

### Determining a Triangle's Area from Its Three Sides

When you know the length of a triangle’s three sides and you don’t know an altitude, you can use Hero’s formula to find the area. Check it out:

### Determining the Area of an Equilateral Triangle

To calculate a triangle’s area — for most types of triangles — you need to know the triangle’s base and height. However, with an equilateral triangle, all you need to know is the length of one of its sides

### How to Find the Centroid of a Triangle

The three medians of a triangle intersect at its centroid. The centroid is the triangle’s balance point, or center of gravity. (In other words, if you made the triangle out of cardboard, and put its centroid

### Applying the Pythagorean Theorem

The Pythagorean Theorem has been known for at least 2,500 years. You use the Pythagorean Theorem when you know the lengths of two sides of a right triangle and you want to figure out the length of the