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Triangles

The Hook

The strongest shape.

What is it?

A polygon with three edges and three vertices. Internal angles always sum to 180°.

Time Travel (History)

The strongest structure in architecture because it cannot change shape without breaking a side.

Cheat Code

All angles inside MUST add up to 180 degrees.

Practice This Now!

The Field Guide

In Plain English: Triangles are the bedrock of shapes. Unlike a square, which can tilt into a diamond, a triangle is rigid. That is why bridges are made of them.

In The Real World: Construction. Roof trusses are triangles to prevent the roof from collapsing.

How To Do It

  1. Identify the missing angle.
  2. Add the two known angles together.
  3. Subtract that sum from 180.
  4. The result is your missing angle.

Booby Trap!

Assuming a triangle is a Right Triangle just because it looks like one. Never assume 90 degrees unless you see the little square box.

Real World Challenge
"A triangle has angles of 50° and 60°. What is the third angle?"
The Logic: 50 + 60 = 110. Total must be 180. 180 - 110 = 70 degrees.

Training Drills

Sum Theorem
/\ /__\ A+B+C = 180
Always 180.