Let's Break it Down
In this lesson, you will learn how to identify different types of triangles. All triangles share two characteristics, no matter what type of triangle you are dealing with.
Basic Triangle Characteristics
Triangles ALWAYS have 3 angles.
Triangles ALWAYS have 3 sides.
Triangle are classified based on the interior angle measurements and side lengths. Click each topic to learn more.
The interior angles of a triangle are the three angles on the inside of the triangle. Look at the triangles in the table below.
First triangle: An acute triangle with angle measurements of 58 degrees, 44 degrees, and 78 degrees. Second triangle: An obtuse triangle with an angle measurement of 130 degrees. Third Triangle: A right triangle with an angle measurement of 90 degrees.
Even though each one is a triangle, they are all different types as described in the table below.
| Acute Triangle |
A triangle whose \(3\) interior angles are all less than \(90^\circ\). |
|---|---|
Obtuse Triangle |
A triangle that has \(1\) interior angle greater that \(90^\circ\). |
Right Triangle |
A triangle that has \(1\) interior angle equal to \(90^\circ\). |
Acute, obtuse, and right triangles are distinguishable by their interior angles. Triangles can also be distinguished by their side lengths. Look at the triangles below.
First Triangle: An equilateral triangle with all sides measuring 2. Second Triangle: An isosceles triangle with two sides measuring 2.24 and the base measuring 4. Third Triangle: A scalene triangle with sides measuring 3.25, 2.82, and 1.55.
Even though each one is a triangle, they are all different types as described in the table below.
| Equilateral Triangle |
A triangle that has side lengths that are all equal (and interior angle measurements that are all congruent). |
|---|---|
Isosceles Triangle |
A triangle that has two side lengths that are equal (and two interior angles that are congruent). |
Scalene Triangle |
A triangle that does not have any side lengths that are equal (and no interior angles that are congruent). |
Marking Sides and Angles Congruent
The congruence of corresponding line segments is shown by marking the line segments with the same number of tick marks (these are sometimes called hash or hatch marks). So, a tick mark denotes side measurements of equal length.
The congruence of the corresponding angles is shown by marking the angle with the same number of rounded arcs, except in the case of a right angle. Recall that right angles are always marked with the right-angle symbol. So, a \(90^\circ\) angle measurement is represented using a square instead of an arc.
Think you got it?
Practice identifying different types of triangles by completing the activity below. Select the triangle that answers each question.
Which is an obtuse triangle?
An obtuse triangle is any triangle that has one interior angle greater than \(90^\circ\). This is an acute triangle.
An obtuse triangle is any triangle that has one interior angle greater than \(90^\circ\). This is a right triangle.
An obtuse triangle is any triangle that has one interior angle greater than \(90^\circ\).
Which is an isosceles triangle?
An isosceles triangle has two sides that are equal. This is an equilateral triangle.
An isosceles triangle has two sides that are equal.
An isosceles triangle has two sides that are equal. This is a scalene triangle.
Which is an equilateral triangle?
An equilateral triangle has all side measurements equal.
An equilateral triangle has all side measurements equal. This is an isosceles triangle.
An equilateral triangle has all side measurements equal. This is a scalene triangle.
Which is a right triangle?
A right triangle is a triangle that has one interior angle of 90°. A 90° angle measurement is represented using a square. This is an obtuse triangle.
A right triangle is a triangle that has one interior angle of 90°. A 90° angle measurement is represented using a square. This is an acute equilateral triangle.
A right triangle is a triangle that has one interior angle of 90°. A 90° angle measurement is represented using a square.
Which is a scalene triangle?
A scalene triangle is a triangle that does not have any side lengths that are equal. This is an isosceles triangle.
A scalene triangle is a triangle that does not have any side lengths that are equal.
A scalene triangle is a triangle that does not have any side lengths that are equal. This is an equilateral triangle.
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