# Classifying Triangles in Geometry

## Understanding Triangles

A triangle is a three-sided polygon, meaning that it has three sides and three angles. The sides of a triangle are usually referred to as side A, side B, and side C. The angles of a triangle are usually referred to as angle A, angle B, and angle C. Every triangle has three sides and three angles, ranging from 0 to 180 degrees.

When classifying triangles, it is important to remember that the angles and the sides of a triangle can vary in size and shape. For example, a triangle can be either scalene, isosceles, or equilateral. A scalene triangle is a triangle with three unequal sides, while an isosceles triangle is a triangle with two equal sides and two equal angles. An equilateral triangle is a triangle with three equal sides and three equal angles.

## Classifying Triangles by Sides

The first way to classify a triangle is by the length of its sides. A triangle can be classified as scalene, isosceles, or equilateral depending on the length of its sides. A scalene triangle is a triangle with three unequal sides. An isosceles triangle is a triangle with two equal sides, and an equilateral triangle is a triangle with three equal sides.

When classifying a triangle by its sides, it is important to remember that all three sides must be measured before the triangle can be accurately classified. For example, if two sides of the triangle are equal in length, then the triangle is an isosceles triangle, but if all three sides are equal in length, then the triangle is an equilateral triangle.

## Classifying Triangles by Angles

The second way to classify a triangle is by the measure of its angles. A triangle can be classified as acute, right, or obtuse depending on the measure of its angles. An acute triangle is a triangle with three angles that measure less than 90 degrees. A right triangle is a triangle with one angle that measures exactly 90 degrees, and an obtuse triangle is a triangle with one angle that measures more than 90 degrees.

When classifying a triangle by its angles, it is important to remember that all three angles must be measured before the triangle can be accurately classified. For example, if two angles of the triangle measure less than 90 degrees, then the triangle is an acute triangle, but if one angle of the triangle measures exactly 90 degrees, then the triangle is a right triangle.

## Classifying Triangles by Sides and Angles

The third way to classify a triangle is by both the length of its sides and the measure of its angles. A triangle can be classified as acute scalene, acute isosceles, acute equilateral, right scalene, right isosceles, right equilateral, obtuse scalene, obtuse isosceles, or obtuse equilateral depending on the length of its sides and the measure of its angles.

When classifying a triangle by both its sides and its angles, it is important to remember that both the sides and the angles must be measured before the triangle can be accurately classified. For example, if two sides of the triangle are equal in length and two angles of the triangle measure less than 90 degrees, then the triangle is an acute isosceles triangle, but if three sides of the triangle are equal in length and one angle of the triangle measures exactly 90 degrees, then the triangle is a right equilateral triangle.

## Practice Problems

1. Classify the triangle with sides of length 5, 7, and 8:

Answer: This triangle is a scalene triangle.

2. Classify the triangle with angles of measure 60, 60, and 60:

Answer: This triangle is an equilateral triangle.

3. Classify the triangle with sides of length 3, 3, and 4:

Answer: This triangle is an isosceles triangle.

4. Classify the triangle with angles of measure 35, 95, and 50:

Answer: This triangle is an obtuse triangle.

5. Classify the triangle with sides of length 6, 6, and 8:

Answer: This triangle is a right isosceles triangle.

6. Classify the triangle with angles of measure 45, 45, and 90:

Answer: This triangle is a right triangle.

7. Classify the triangle with sides of length 5, 7, and 6:

Answer: This triangle is an acute scalene triangle.

8. Classify the triangle with angles of measure 40, 40, and 100:

Answer: This triangle is an obtuse isosceles triangle.

9. Classify the triangle with sides of length 7, 7, and 7:

Answer: This triangle is an equilateral triangle.

10. Classify the triangle with angles of measure 70, 50, and 60:

Answer: This triangle is an acute triangle.

## Summary

In this lesson, we discussed how to classify triangles in geometry. We discussed the three different ways to classify a triangle: by its sides, by its angles, or by both its sides and its angles. We also looked at several practice problems to help us better understand how to classify triangles. Remember, when classifying a triangle, it is important to measure both the sides and the angles of the triangle before classifying it accurately.

## FAQ

### What are the 4 ways to classify a triangle?

Triangles can be classified in four ways: by the lengths of their sides, by their angles, by the number of sides that are equal, and by the type of angles they possess (acute, obtuse, or right).

### What are the 6 words that classify triangles?

The six words that classify triangles are equilateral, isosceles, scalene, acute, obtuse, and right.

### What are 3 ways to classify a triangle by its sides?

Triangles can be classified by their sides as equilateral (all sides equal length), isosceles (two sides equal length), or scalene (all sides unequal length).

### How do you classify a triangle by its points?

Triangles can be classified by their points as acute (all angles less than 90 degrees), obtuse (one angle greater than 90 degrees), or right (one angle equal to 90 degrees).