Understanding the properties of triangles is really important for learning key ideas in geometry. It helps us see the differences between triangles based on their sides and angles.

Types of Triangles:

1. By Sides:

   • Equilateral: All three sides are the same length. Each angle measures $60^\circ$.
   • Isosceles: Two sides are the same length. The angles opposite those sides are also the same.
   • Scalene: All sides and angles are different lengths and sizes.

2. By Angles:

   • Acute: All angles are smaller than $90^\circ$.
   • Right: One angle is exactly $90^\circ$.
   • Obtuse: One angle is greater than $90^\circ$.

Knowing the different types of triangles helps us understand some bigger ideas in geometry, like congruence and similarity.

One important rule is called the Pythagorean theorem. This rule says that in a right triangle, the squares of the two shorter sides ($a$ and $b$) add up to equal the square of the longest side ($c$). This gives us a way to figure out distances in math problems dealing with shapes and locations.