A triangle is a shape with three straight sides and three corners, or vertices. It's the simplest possible polygon, but it's also one of the strongest and most important shapes in geometry and engineering.

Every triangle has a fundamental property: its three interior angles always add up to 180 degrees. It doesn’t matter if the triangle is long and skinny or perfectly balanced. The sum is always $180^{\circ}$.

We can categorize triangles based on the lengths of their sides. This gives us three main types.

An equilateral triangle has three equal sides and three equal angles, each measuring $60^{\circ}$.

An isosceles triangle has two equal sides. The angles opposite these equal sides are also equal to each other.

A scalene triangle has no equal sides. All three of its sides and all three of its angles are different.

Every triangle has several different "center" points, each found in a unique way and having special properties. Let's look at four of the most common ones.

A median is a line from a vertex to the midpoint of the opposite side. The point where the three medians meet is the centroid. If you were to cut a triangle out of cardboard, it would balance perfectly on its centroid.

A perpendicular bisector is a line that cuts a side in half at a perfect 90-degree angle. The circumcenter, where these three lines meet, is the center of a circle that passes through all three of the triangle's vertices.

An angle bisector is a line that splits an angle into two equal smaller angles. Where they meet is the incenter, which is the center of a circle that can be drawn perfectly inside the triangle, just touching all three sides.

Finally, an altitude is a line from a vertex that is perpendicular to the opposite side. The point where the three altitudes intersect is the orthocenter. We'll explore altitudes in more detail later on.

Time to check your understanding of these basic concepts.

These building blocks are the foundation for understanding more complex geometric ideas.