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 that ΔEGF and ΔHKJ  are congruent.

So, first writing the congruency of the triangle

As ∠E=∠H=45°  and ∠G=∠K=90°

Corresponding angles of ∠E and ∠G are ∠H and ∠K respectively.

Therefore, ΔEGF ≅ ΔHKJ

As the corresponding parts of the congruent triangles are equal

So, EG=HK, GF=KJ

, and EF=HJ.

From the figure,  GF=3a, and KJ=b

So, 3a=b

Therefore, a=3/b...(i)

Similarly, from the figure, EF=6, and HJ=b√2

So, b√2=6

Therefore, b=6/√2=3√2...(ii)

Putting the value of b from equation (ii) to equation (i), we have,

a=3/(3√2)=√2

Hence, the value of a is √2.