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Triangles

Overview

The strongest shape.

What is it?

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

History

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

Key Idea

All angles inside MUST add up to 180 degrees.

Practice This Topic

Concept Guide

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.

Real-world example: 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.
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Common Pitfall

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

Word Problem
"A triangle has angles of 50° and 60°. What is the third angle?"
Reasoning: 50 + 60 = 110. Total must be 180. 180 - 110 = 70 degrees.

Practice Examples

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