Congruent Triangles: SSS, SAS, ASA, AAS

Congruent triangles are exactly the same size and shape. You do not need to measure every side and angle if a congruence shortcut applies.

Quick idea

SSS, SAS, ASA, and AAS are enough information to prove two triangles congruent.

Steps

1. Mark the given equal sides and angles.
2. Check which congruence shortcut fits the pattern.
3. Make sure the included side or angle requirement is satisfied when using SAS or ASA.
4. Write the congruence statement in matching order.

Worked example

Write a congruence statement for matching triangles.

Full solution

Step-by-step walkthrough

Step 1

The first letters match corresponding vertices.

Step 2

AB matches DE, BC matches EF, and AC matches DF.

Step 3

The order matters because it tells which parts correspond.

Common mistake

AAA proves similarity, not congruence. Equal angles alone do not guarantee equal side lengths.

Practice problems

1. Does SSS prove congruence?
2. Does AAA prove congruence?
3. In SAS, what must be true about the angle?

Answers

1. Yes
2. No
3. It must be between the two known sides

Ask Pennpaper to explain it live

If the steps make sense but you still feel stuck, start a Pennpaper lesson and ask the tutor to draw the problem on the whiteboard. Seeing the symbols move step by step is often what makes the concept click.

Related guides

• Similar Triangles Explained
• How to Find Missing Angles
• Pythagorean Theorem Explained