Types of triangles

A triangle is the simplest closed shape with straight sides , three sides, three corners, three angles. Yet there are many kinds of triangles, each with its own name based on how its sides or angles compare.

What is this?

We sort triangles two ways: by their sides and by their angles.

By sides:

• Equilateral triangle , all three sides equal. All three angles also equal (each 60°). Looks like the shape of a samosa or a road-sign warning.
• Isosceles triangle , exactly two sides equal. The two angles facing those equal sides are also equal.
• Scalene triangle , all three sides different. No equal angles either.

By angles:

• Acute triangle , all three angles less than 90°. Looks "sharp" everywhere.
• Right triangle , exactly one angle of 90°. Looks like the shape of a set-square.
• Obtuse triangle , exactly one angle bigger than 90°. Has one wide, "lazy" corner.

Each triangle has both a side-name and an angle-name. For example, the corner cut from a square is an isosceles right triangle , two equal sides and one right angle.

There is one big rule for triangles: the three angles always add up to 180°. So if one angle is 90° and another is 60°, the third must be 30°.

Worked examples

Example 1. A triangle has sides 5 cm, 5 cm, 5 cm. What kind?

• All sides equal → equilateral.

Example 2. A triangle has one angle of 90°, another of 45°. Third?

• 180 − 90 − 45 = 45°.
• Two equal angles (45° and 45°) → isosceles. Also right-angled. So: isosceles right triangle.

Example 3. A triangle has angles 30°, 60°, 90°. Type by angle?

• One angle is 90° → right triangle.

Try it

1. Name the triangle: sides 3 cm, 4 cm, 5 cm.
2. Name the triangle: angles 80°, 60°, 40°.
3. Two angles of a triangle are 50° and 70°. Find the third.
4. A triangle has angles 110°, 40°, 30°. What kind by angles?
5. Can a triangle have two right angles? Explain.

Hands-on

Triangle hunt. Find at least 5 triangles in your home or school. Sort them by side type , equilateral, isosceles, or scalene.

Paper cutting. Cut a square into two triangles along the diagonal. What kind of triangle did you make? (Right-angled and isosceles.) Now cut an equilateral paper triangle into two , what do you get?