FORMULABANK

Similar Figures

Two figures are similar if one figure is either an enlargement or an exact copy of the other figure. The two figures can be rotated or mirrored relative to each other.

Two triangles are similar if:

• At least 2 of the angles in both triangles are pairwise equal.
• All 3 side lengths in one triangle have the same ratio to the corresponding side lengths in the other triangle.

Congruent Figures

Two figures are congruent if one figure is an exact copy of the other figure. The two figures can be rotated or mirrored relative to each other.

Two triangles are congruent if:

• The sides are pairwise equal.
• Two sides are pairwise equal and the included angle is equal.
• One side and the adjacent angles are pairwise equal.

Examples:

Triangle 1 and Triangle 2 are congruent.
Triangle 1, 2, and 3 are similar.
Triangle 4 is neither similar nor congruent with the other 3 triangles.

Sketches of Triangles