More Examples of Types of Triangles

In this page we practice identifying different types of triangles based on their angles and side lengths.

Example 1 – Acute Triangle

\(\text{Angles: } 70^\circ, 60^\circ, 50^\circ\)

All angles are less than \(90^\circ\), so this triangle is an acute triangle.

\(\text{Angles: } 90^\circ, 45^\circ, 45^\circ\)

Because one angle is \(90^\circ\), this triangle is a right triangle.

\(\text{Angles: } 130^\circ, 30^\circ, 20^\circ\)

One angle is greater than \(90^\circ\), so this triangle is an obtuse triangle.

\(\text{Angles: } 110^\circ, 40^\circ, 30^\circ\)

All sides are different, which means all angles are different.
This triangle is a scalene triangle.

Two sides are equal.

Because the sides are equal, the angles opposite those sides are also equal.
This triangle is an isosceles triangle.

All three sides are equal.

Since the sum of the angles of a triangle is \(180^\circ\), we can write:

\(x + x + x = 180^\circ\)

\(3x = 180^\circ\)

\(x = 60^\circ\)

So an equilateral triangle has three \(60^\circ\) angles.

Can the following side lengths form a triangle?

\(1, 2, 2 \quad \longrightarrow \quad\) True (Because \(1 + 2 > 2\))
\(2, 2, 2 \quad \longrightarrow \quad\) True (Because \(2 + 2 > 2\))
\(1, 1, 3 \quad \longrightarrow \quad\) False (Because \(1 + 1 < 3\))
\(1, 2, 3 \quad \longrightarrow \quad\) False (Because \(1 + 2 = 3\))
\(4, 5, 6 \quad \longrightarrow \quad\) True (Because \(4 + 5 > 6\))
\(3, 3, 5 \quad \longrightarrow \quad\) True (Because \(3 + 3 > 5\))
\(5, 9.5, 5 \quad \longrightarrow \quad\) True (Because \(5 + 5 > 9.5\))
\(5, 9.9, 5 \quad \longrightarrow \quad\) True (Because \(5 + 5 > 9.9\))
\(5, 5, 10 \quad \longrightarrow \quad\) False (Because \(5 + 5 = 10\))

When the sum of two sides equals the third side, the shape collapses into a straight line, so it is not a triangle.