Congruent Triangles

When two triangles are congruent they will have exactly the same three sides and exactly the same three angles. The equal sides and angles may not be in the same position (if there is a turn or a flip), but they are there.

SSS stands for "side, side, side" and means that we have two triangles with all three sides equal. For example: is congruent to: (See Solving SSS Triangles to find out more) If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

SAS (side, angle, side)If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.

angle, side, angleASA (angle, side, angle)If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

RHS Congruence RuleTheorem: In two right-angled triangles, if the length of the hypotenuse and one side of one triangle, is equal to the length of the hypotenuse and corresponding side of the other triangle, then the two triangles are congruent.