TTinkerwise
Unlock all
math / Geometry / free

Euclidean Geometry

Turn points, lines, and angles into invariants you can see and prove.

Follow the mechanism1 / 3

Three rays enclose a triangle. Three line segments meet pairwise to create three corners and three interior angles.

triangle constructionacute · angles sum to 180°
Focus the idea
The interior angles of a triangle add to 180 degreesA acute triangle has angles 55, 65, and 60 degrees, with a total of 180 degrees. A · 55°B · 65°C · 60°A + B + C = 180°
angle A55°
angle B65°
angle C60°
triangleacute

The third angle is not independent: once A and B are chosen, C must be 60° so the total stays 180°.

Euclidean geometry turns a visual construction into an invariant: in every flat triangle, the interior angles add to 180 degrees. The triangle scales to stay on-screen; the proof relationship is unchanged.