The triangles EFG and HJK are congruent as all three sides of triangle EFG are given equal to the three sides of triangle HJK.
The postulate applied here is Side-Side-Side (SSS) postulate.
Thus, we can select option A. Congruent - SSS.
When are two triangles congruent?
Two triangles are congruent when their shape is identical and their size is equal, that is, the three sides are equal and the three angles are also equal.
Congruency in triangles can be proven by the following postulates:
- Side-Side-Side (SSS) postulate: When all three sides are equal.
- Side-Angle-Side (SAS) postulate: When two sides are equal and the angle containing them is also equal.
- Angle-Side-Angle (ASA) postulate: When two angles and the side common to them are equal.
- Angle-Angle-Side (AAS) postulate: When two angles and a non-included side are equal to the corresponding part.
- Right-Hypotenuse-Side (RHS) postulate: In a right triangle, the hypotenuse and a side are equal.
How to solve the question?
In the question, we are asked if EFG - HJK (EFG is congruent to HJK), when we are given that:
EF = HJ
EG = HK
FG = JK.
And if they are congruent, by which postulate it is so.
The triangles EFG and HJK are congruent as all three sides of triangle EFG are given equal to the three sides of triangle HJK.
The postulate applied here is Side-Side-Side (SSS) postulate.
Thus, we can select option A. Congruent - SSS.
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