Similar triangles

Similarity is a generalisation of congruence: two similar figures have the same shape but not necessarily the same size. The fundamental case is that of triangles.

Definition — Similar triangles

Two triangles are similar if they have respectively congruent angles and corresponding sides in proportion (ratio of similarity $k$).

The number $k$ is the ratio of similarity: it indicates how many times each side of one triangle is larger than the corresponding side of the other. If $k=1$ the two triangles are congruent.

Explore the definition with the simulation: drag the vertices of the green triangle and vary the scale factor $k$ — the red triangle always stays similar and its angles do not change.

Drag the vertices $A$, $B$, $C$ and move the slider $k$.

Links

Topics: Similarity
Concepts: Ratio of similarity · Similarity · Similar triangles
Skills: Synthetic geometry