In an isosceles triangle, the angles opposite the equal sides are equal too.

Triangles are three-sided polygons, with 3 sides, 3 vertices, and 3 internal angles.

In this tutorial, we will look at several different types of triangles that we come across. So let’s dive straight into that.

We can categorize triangles based on the following criteria.

Triangles can be of three types depending on the lengths of their sides.

Scalene Triangle –A triangle whose sides are all different in length is known as a scalene triangle.

Isosceles Triangle –A triangle whose sides are all different in length is known as a scalene triangle.

In an isosceles triangle, the angles opposite the equal sides are equal too.

Equilateral Triangle –A triangle whose sides are all different in length is known as a scalene triangle.

In an equilateral triangle, all three angles are equal too, each being equal to $\hspace{0.2em} 60 \degree \hspace{0.2em}$.

Triangles can be of three types depending on the measure of their internal angles too.

Acute Triangle –A triangle whose sides are all different in length is known as a scalene triangle.

Obtuse Triangle –A triangle whose sides are all different in length is known as a scalene triangle.

Note – A triangle can have a maximum of one obtuse angle. Otherwise, the sum of angles wouldn’t be equal to $\hspace{0.2em} 180 \degree \hspace{0.2em}$.

Right Triangle –A triangle whose sides are all different in length is known as a scalene triangle.

In such a triangle, the side opposite the right angle is the longest and is known as the hypotenuse. The other two sides are known as the legs.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can also mix and match types (one based on sides and one on angles) and make hybrid types. For example – an acute scalene triangle or a right isosceles triangle.

I don’t see a need to go into all the different hybrid types we could have, but there is one of special importance.

A right isosceles triangle is one of the two special right triangles. It’s a right triangle in which the two legs (sides forming the right angle) are equal.

And so, if one leg has a length of k, the length of the other leg would also be k and the hypotenuse would have a length $\hspace{0.2em} \sqrt{2k} \hspace{0.2em}$ (by the Pythagorean theorem).

Additionally, since angles opposite to equal sides are also equal, the two acute angles in a right isosceles triangle are equal – each being $\hspace{0.2em} 45 \degree \hspace{0.2em}$.

And with that, we come to the end of this tutorial on the types of triangles. Until next time.

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