TwiddleLab / Math / Shapes and Proof

Why Triangles Add to 180

Lesson 1 of 10 · 5 min · Free, no account needed

What you will learn

• The three angles of any triangle add to 180°.
• A straight line is a straight angle: 180°. Three torn corners fill it with no gap.
• Missing angle = 180° minus the two you know.

Start the lesson

How the lesson goes

1. Any triangle, as weird as you like. Its three angles always add to the same number.

   Which number? Drag the lever to your bet.

2. Tear off the three corners. Lay them on the line.

   Drag each torn corner onto the dot. They line up side by side.

3. Maybe that triangle was special. Stretch it.

   Drag the corners and make the three shapes on the list. Watch the line.

4. Two names for what you saw.

   A straight line is a straight angle: half a turn, 180°.

   The three torn corners always fill it. So the angle sum of any triangle is 180°.

   That gives a quick tool: missing angle = 180° minus the other two.

5. Make your own right triangle.

   Drag the top corner until its angle is exactly 90°. Any shape you like.

   With one corner at 90°, the other two share the remaining 90°: they always add to 90°.

6. Game: find the missing angle.

   Set the blue slice so it closes the line exactly, then Place it. Four triangles, fewest misses wins.

7. One last time, with your own triangle.

   Tap each corner to tear it off.

Next lesson: Same Shape, Same Size · Part of the course: Shapes and Proof

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