Triangle Congruence Criteria

Run Fullscreen

About This Diagram

This diagram illustrates the five ways to prove triangles congruent, plus shows why AAA (three angles) is NOT sufficient.

Valid Criteria (Sufficient for Congruence)

Criterion	Name	What to Show
SSS	Side-Side-Side	Three pairs of sides congruent
SAS	Side-Angle-Side	Two sides and included angle congruent
ASA	Angle-Side-Angle	Two angles and included side congruent
AAS	Angle-Angle-Side	Two angles and non-included side congruent
HL	Hypotenuse-Leg	Right triangles: hypotenuse and one leg congruent

Invalid Criteria (NOT Sufficient)

Criterion	Why It Fails
AAA	Same angles means similar, not congruent (size can differ)
SSA	Ambiguous case - two different triangles possible

Interaction

Click any criterion button (SSS, SAS, ASA, AAS, HL, AAA) to see an example with marked congruent parts.

Learning Objectives

• Identify which congruence criterion applies
• Evaluate whether given information is sufficient for congruence

Bloom's Taxonomy Level

Understanding and Evaluating - Recognizing valid criteria.

Iframe Embed Code

<iframe src="https://dmccreary.github.io/geometry-course/sims/triangle-congruence-criteria/main.html"
        height="552px"
        width="100%"
        scrolling="no"></iframe>