Functions
AI Assistant

Congruence & Similarity

Same shape? Same size? How to tell — and why it matters

Congruent figures have the same shape AND the same size — you can slide, rotate, or flip one to match the other exactly. Similar figures have the same shape but can be different sizes — one is a scaled copy of the other.

The graph shows two triangles. Are they congruent? Similar? The AI will help you measure sides and angles to find out, using the classic tests: SSS (all three sides match), SAS (two sides and the angle between), and AA (two angles match — for similarity).

Ask the AI "Are these triangles congruent?" or "What's the scale factor?"

Graph

FAQ

What does congruent mean?
Two figures are congruent if they have exactly the same shape and size. All corresponding sides are equal, and all corresponding angles are equal. You can move one figure (translate, rotate, or reflect) to land perfectly on the other.
What does similar mean?
Two figures are similar if they have the same shape but possibly different sizes. All corresponding angles are equal, and corresponding sides are proportional (same ratio). The ratio of corresponding sides is called the scale factor.
What are the triangle congruence tests?
SSS (three sides match), SAS (two sides and included angle match), ASA (two angles and included side match), AAS (two angles and a non-included side match). These are shortcuts — you don't need to check all six measurements.
Where is similarity used in real life?
Maps use similar figures (the map is a scaled-down version of the territory). Shadow problems use similar triangles to find heights. Architects use scale models. Photo enlargements preserve similarity.

Related Topics

Pythagorean TheoremRatios & ProportionsIntro to Trigonometry