Rules for Triangle Congruence


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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 is equal to the corresponding three sides of other 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 right-angled triangle and hypotenuse and one side of one triangle is equal to the hypotenuse and corresponding side of other 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.

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