Answer:
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
The given triangles are congruent by AAA . and the value of a = √2.
The two triangle has prove to be congruent and value of a to be determine. Both the triangle are right angle triangles.
Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.
since, the sum of the angles in triangle is 180
In triangle Angle G, E, and F
G + F +E =180
90 + 45 + E = 180
Angle E = 45
similarly Angle J = 45
Triangle GEF and Triangle HKJ
Angle G = Angle K (both are of 90)
Angle F = Angle H (both are of 45)
Angle E = Angle J (both are of 45)
So, Triangle GEF and Triangle HKJ are congruent triangles by AAA congruency.
Now in triangle GEF
cos 45 = 3a/6
1/√2 = a/2
a = √2
Thus, the given triangles are congruent by AAA . and the value of a = √2.
Learn more about similar triangles here:
brainly.com/question/25882965
#SPJ2
