lesson
Updated 1 month ago · 6 views
If you rip the three corners off any paper triangle and line them up side by side, they will always form a perfectly flat straight line.
📊Interactive animation showing a colorful triangle with vertices labeled A (blue), B (orange), and C (green). The three corner tips detach, rotate, and snap together along a horizontal straight line with a protractor showing the total angle measures exactly 180 degrees. Includes a 'Replay' button. Clean card style, responsive layout, readable fonts.
Why does this happen for every single triangle, regardless of its shape?
The Triangle Angle Sum Theorem
The Triangle Angle Sum Theorem states that the interior angles of any triangle in a flat plane always add up to exactly 180∘.
Around 300 BCE, the Greek mathematician Euclid proved this by drawing a line through one vertex parallel to the opposite side.
📊Geometric proof diagram of Triangle ABC. A dashed line parallel to base AC passes through the top vertex B. Show alternate interior angles: angle at bottom-left A matches top-left angle 1, angle at bottom-right C matches top-right angle 3, and angle B sits in the middle. The three angles form a straight line at vertex B, visually demonstrating angle 1 + angle B + angle 3 = 180 degrees.
Since all three interior angles sum to 180∘, knowing any two angles means the third angle is locked in.
How do we turn this relationship into a reliable calculation step?
Finding the Unknown Angle
To find a missing angle x, add the two known angles together and subtract that sum from 180∘.
x=180∘−(∠A+∠B)
Let's work through an example: suppose a triangle has angles measuring 65∘ and 45∘.