Triangles are really interesting! Just three sides can create different shapes, and each type has its own special features. Let’s look at the main types of triangles: equilateral, isosceles, and scalene.

Equilateral Triangles

• Definition: All three sides are equal.
• Angles: Each angle is 60 degrees. So, not only are the sides the same, but the angles are too!
• Symmetry: Equilateral triangles are very balanced. You can draw several lines through each corner, which makes them nice to look at.

Isosceles Triangles

• Definition: Two sides are the same length, and the third side is different.
• Angles: The angles across from the two equal sides are also equal. If two sides are the same, the angles across from them will match too.
• Symmetry: Isosceles triangles have one line of symmetry. This line goes from the top point down through the base, splitting the triangle in half perfectly.

Scalene Triangles

• Definition: All three sides are different lengths. No sides or angles are the same.
• Angles: The angles in a scalene triangle can be different too. They can be acute (small), right (90 degrees), or obtuse (large). It’s fun because you can’t tell what the angles are just by looking at the sides.
• Symmetry: Scalene triangles don’t have any lines of symmetry. They might seem a little uneven, but that’s what makes them unique!

Pythagorean Theorem

When you think about triangles, especially right-angled ones, remember the Pythagorean theorem. This rule tells us that in a right triangle, if you take the longest side (the hypotenuse, which we call $c$) and square its length, it will equal the sum of the squares of the other two sides ($a$ and $b$). We can write this as:

$$c^2 = a^2 + b^2$$

Understanding these triangle types and properties is really helpful. Whether you are solving math problems, learning new theorems, or simply enjoying different shapes, triangles have a lot to offer! It’s amazing how these simple forms can have such meaningful math features.