Congruent Triangles
Same shape and size: SSS, SAS, ASA, AAS, HL.
Key idea
Same shape and size: SSS, SAS, ASA, AAS, HL.
In depth
Congruent triangles have the same shape and size. You do not need to compare all six parts: SSS, SAS, ASA, AAS and RHS are enough. SSA is not sufficient in general.
Worked example
Two triangles with sides 3, 4, 5 are congruent by SSS.
Real-world uses
- Checking identical roof trusses or copied parts in manufacturing
- Proving two shapes are the same
Common mistake
Using SSA (or AAA). Equal angles alone give similar, not congruent, triangles.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Congruent Triangles?
Same shape and size: SSS, SAS, ASA, AAS, HL. It is a topic at the intermediate level in Geometry.
Where is Congruent Triangles used in real life?
Real-world examples: Checking identical roof trusses or copied parts in manufacturing; Proving two shapes are the same.
What should I learn before Congruent Triangles?
Make sure you are comfortable with Triangle Inequality, the previous topic in Geometry.
What is a common mistake with Congruent Triangles?
Using SSA (or AAA). Equal angles alone give similar, not congruent, triangles.
How can I practise Congruent Triangles?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Congruent Triangles?
Move on to Similar Triangles next.
Related intermediate topics in Geometry
- Vertical Angles – Opposite angles formed by intersecting lines are equal.
- Parallel Lines and Transversals – Corresponding and alternate interior angles are equal.
- Exterior Angle Theorem – An exterior angle equals the sum of the two remote interior angles.
- Triangle Inequality – Any two sides sum to more than the third.
- Similar Triangles – Same shape, proportional sides: AA, SAS~, SSS~.
- Pythagorean Theorem – In a right triangle the squares on the legs sum to the square on the hypotenuse.