📐 Getting to Know Triangles: By Sides and Angles

Hello! Today we are exploring the world of triangles. Every triangle has two names: one from its sides and one from its angles. Let’s meet them!

A triangle has 3 vertices (corners), 3 sides and 3 angles. The vertices are points. The sides are the straight lines that join the vertices. The angles are made at the vertices.

Let’s look at the sides first. A triangle with all three sides equal is equilateral. A triangle with two equal sides is isosceles. A triangle with all three sides different is scalene. We show equal sides with the same number of tick marks.

Let’s lay the sides side by side as strips. Strips of the same length have the same colour. If all three strips match, the triangle is equilateral. If two strips match, it is isosceles. If none match, it is scalene.

Now let’s look at the angles. If all three angles are less than 90°, it is acute-angled. If one angle is exactly 90°, it is right-angled, and we draw a small square in that corner. If one angle is more than 90°, it is obtuse-angled.

Let’s cut off the corners of a triangle and line them up. 30°, 30° and 120° make a straight line: 180°. In every triangle, the three angles add up to 180°. That is why a triangle can have at most one right angle or obtuse angle.

We give the same triangle two names: one from its sides and one from its angles. The one on the left is both equilateral and acute-angled. The one in the middle is both scalene and right-angled. The one on the right is both isosceles and obtuse-angled.

What happens if we drag a corner? As the top corner slides to the left, the angle on the left gets bigger. First the triangle is acute-angled, then right above the corner it is right-angled, then obtuse-angled. The corner moved, and the triangle’s name changed too!

A triangle is a polygon. A polygon is a closed shape with straight sides. We call a shape with 3 sides a triangle, 4 sides a quadrilateral, 5 sides a pentagon and 6 sides a hexagon. It has as many vertices and angles as sides. An open line is not a polygon.

Summary: every triangle has one name from its sides and one from its angles. Its angles always add up to 180°. Now try it in Angle Hunter!