Find the value of a that satisfies the congruency of the triangles. In two or more complete sentences, explain the relevance between the congruency of the triangles and the calculations made in finding the value of a.

a=√2

Step-by-step explanation:

Given : ΔEGF ≅ ΔHKJ

where ∠G=∠K [right angle]

∠E=∠H=45°

And ∠F=180°-∠E-∠G [By angle sum property]

⇒∠F=180°-45°-90°

⇒∠F=45°=∠J  [corresponding parts of two congruent triangles are congruent]

⇒ Both triangles are isosceles right triangles such that

JK=HK=b , EG=GF

and EF=JH

Now JK=HK= EG=GF=3√2

Now GF=3a=3√2

⇒a=√2