Kinds of triangles

A triangle has names by sides and by angles

The geometry part of Percent kid starts. The first hero is the triangle — the strongest shape builders know. That is why it holds bridges, cranes and roofs.

We sort triangles in two ways. By sides: equilateral (all three sides the same), isosceles (two the same — they are called the legs), scalene (each different).

By angles: acute (all angles acute, so smaller than 90°), right-angled (one angle exactly 90°), obtuse (one angle bigger than 90°).

Every triangle has a name from both boxes at once — for example a right-angled isosceles. It is like people: a surname by the sides, a first name by the angles. When you describe a triangle, say both.

And one rule you will use all the time: the sum of the interior angles of every triangle is 180°. You know two angles? You calculate the third by subtracting. No exception, no trick — it holds for small and giant triangles, pointy and flat. That rule is what makes it the most reliable shape in all of geometry.

Filip and Jonáš build a set from battens for the school play. A rectangular frame twists into a rhombus. “Add a bar across,” Jonáš advises. Filip screws in a diagonal and the frame suddenly holds. “Why does that work?” — “You made two triangles from a rectangle. A quadrilateral can collapse, a triangle cannot — with three fixed sides you cannot move it.” Filip looks around the hall: triangles in the roof, in a crane outside the window, in a bike stand. “When there is a load-bearing structure, there are triangles,” Jonáš finishes.

Sorting and calculating the third angle

By sides. Equilateral: three equal sides and for free three equal angles of 60° each. Isosceles: two equal legs and a base; the angles at the base are equal. Scalene: no match.

By angles. Acute: all three angles under 90°. Right-angled: one angle exactly 90° (by it are the sides called the legs, opposite the right angle sits the longest side — the hypotenuse). Obtuse: one angle over 90°. A triangle cannot have more than one obtuse or right angle — it would not fit into 180°.

Calculating the third angle: third angle = 180° − first − second. Angles 65° and 40° → the third is 180 − 65 − 40 = 75°.

The triangle inequality. From three segments you make a triangle only when the sum of every two sides is bigger than the third. Sides 3, 4, 8 make nothing: 3 + 4 = 7 < 8, the shorter sides cannot reach each other. Check this always before you start drawing — the next lesson sits on it.

Labelling: vertices with capital letters A, B, C; sides with small a, b, c, where side a sits opposite vertex A.

Find the third angle and the kind of triangle: 90° and 45°

Step 1: third angle: 180 − 90 − 45 = 45°.

Step 2: I sort by angles: one angle is exactly 90° → right-angled.

Step 3: I sort by sides: two angles are equal (45° and 45°) → opposite equal angles sit equal sides → isosceles.

Result: a right-angled isosceles triangle with angles 90°, 45°, 45°. One like that is made when you cut a square along a diagonal.

An isosceles triangle has an angle of 70° at the base. The remaining angles?

Step 1: in an isosceles triangle the angles at the base are equal. The second angle at the base is therefore also 70°.

Step 2: the third angle (at the vertex between the legs): 180 − 70 − 70 = 40°.

Result: 70°, 70°, 40°. Check by adding: 70 + 70 + 40 = 180. That checks out. All angles are under 90°, so it is also an acute triangle.

Can you make a triangle from sides 5 cm, 6 cm and 12 cm?

I test the triangle inequality — the sum of every two sides against the third:

5 + 6 = 11. Is 11 > 12? No.

I do not need to try further — one broken condition is enough.

Result: you cannot make a triangle. The two shorter sides cannot lean towards each other so they touch: even stretched into one line they measure only 11 cm, and the 12 cm gap is longer. If the third side measured 10 cm, the triangle would exist (5 + 6 = 11 > 10).

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. 开始 with ten. When it goes well, add more.

Calculate the third angle. Then say what kind of triangle it is by angles.

Practise the questions

On paper: a gallery of triangles

You will draw and calculate. Get a ruler and a protractor ready.

1. Sketch and label all six kinds: equilateral, isosceles, scalene, acute, right-angled, obtuse. On each mark what gives it its name.

2. Calculate the third angle: a) 35° and 82°, b) 90° and 28°, c) 118° and 31°. For each decide the kind by angles.

3. Decide without drawing which triples of sides make a triangle: a) 4, 5, 6; b) 2, 3, 6; c) 7, 7, 13.

4. Measure with a protractor three angles of any triangle you draw, and check that the sum is 180° (a small measuring error is fine).

Now you 💪

1. I can name the sorting by sides and by angles and I can put a triangle into both.
2. I calculate the third angle by subtracting from 180°.
3. I check the triangle inequality before I start drawing.

What to take from this lesson

• By sides: equilateral, isosceles, scalene.
• By angles: acute, right-angled, obtuse.
• The sum of the interior angles is always 180°.
• Triangle inequality: the sum of two sides must grow past the third.
• A triangle is the strongest shape — that is why it holds bridges and roofs.

© 2026 Ing. Martin Polak / AlgoRhino · 内容使用条款