The Triangle Inequality

Links and useful resources

• gr10's Geometry >>>START HERE<<<
• AoPS Online Textbook
• AoPS Alcumus
• Big Ideas Geometry textbook
• GeoGebra Online Geometry Constuction Tool
• Two-column math templates
• Proofs unit slides from mathgiraffe.com
• Proofs unit printables for two-column proofs

Lesson-specific resource links

Did you know, 10+10 and 11+11 are the same? 10+10 is twenty, and 11+11 is twenty two!
Parallel Lines have a lot in common… It’s a shame they’ll never meet.

• khan academy triangle inequality
• Mario's math triangle inequality

Concept summary and connections

• Triangle Inequality
• The sum of the lengths of the two shorter sides of a triangle is greater than the length of the longer side.

Lesson and worked examples

Follow the proof at AoPS geometry
Follow the proof of altitude ratios here

Media resources

• Youtube search for "Triangle Inequality"
• Youtube search for "The sum of the lengths of the two shorter sides of a triangle is greater than the length of the longer side."

Guided practice

• If we have two segments with lengths 3 and 7, what possible side lengths could we use for a third segment to make a triangle with them?
• Is it possible to have a triangle with side lengths in the ratio 2:4:7?

Homework

• #hw (geom-gr10) 10.3 The Triangle Inequality (p. 274) (gr10) 2025-01-29