Conditions for Congruence of Triangles
Corresponding Sides and Angles in Congruent Figures
Two figures are called congruent if one can completely overlap the other without changing its shape or size.
If
If
In congruent figures, the overlapping vertices, sides, and angles are called corresponding parts.
If
If
- The corresponding vertices are
with , with , and with . - The corresponding sides are
with , with , and with . - The corresponding angles are
with , with , and with .
For congruent figures, the lengths of corresponding sides and the measures of corresponding angles are equal.
Conditions for Congruence of Triangles
Two triangles are congruent in the following cases:
- SSS Congruence: When the lengths of all three pairs of corresponding sides are equal.
- SAS Congruence: When the lengths of two pairs of corresponding sides are equal, and the included angles between these sides are equal.
- ASA Congruence: When the lengths of one pair of corresponding sides are equal, and the measures of the two adjacent angles are equal.
