# Rules for Triangle Congruence

If two triangles are congruent they have equal sides, equal areas.
Condition for congruence:
1. SAS condition If two sides and the included angle of one triangle is equal to the corresponding sides and included angle of the other triangle, then both triangles are congruent.
AB = DE, BC = EF and $\angle$B = $\angle$E, then $\Delta ABC \approx \Delta DEF$

2. ASA condition If two angles and the included side of one triangle is equal to the corresponding two angles and the included side of the other triangle, then both triangles are congruent.
If $\angle$A = $\angle$D, $\angle$B = $\angle$E and AB = DE, then $\Delta ABC \approx \Delta DEF$

3. SSS condition If three sides of one triangle are equal to the corresponding three sides of another triangle then both triangles are congruent.
If AB = DE, AC = DF and BC = EF, then $\Delta ABC \approx \Delta DEF$

4. RHS condition If the two triangles are a right-angled triangle and hypotenuse and one side of one triangle is equal to the hypotenuse and corresponding side of another triangle, then both triangles are congruent.
if $\angle$B =$\angle$E = 90°, AC = DF and AB = DE or BC = EF, then $\Delta ABC \approx \Delta DEF$
Note:
i.   All the congruent triangles are similar but all similar triangles are not congruent.
ii.  The ratio of the areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides.