Given:Two right triangles △ABC and △DEF where ∠B=90∘ and ∠E=90∘, hypotenuse is equal.
i.e., AC=DF and one side is equal i.e.,BC=EF
To prove:△ABC≅△DEF
Proof:In right △ABC
By pythagoras theorem, AC2=AB2+BC2
AB2=AC2−BC2 ........(1)
In right △DEF
By pythagoras theorem, DF2=DE2+EF2
DE2=DF2−EF2 ........(2)
From (1)
AB2=AC2−BC2
⇒AB2=DF2−EF2 since AC=DF and BC=EF
⇒AB2=DE2 from (2)
⇒AB=DE ......(3)
Given:BC=EF,AC=DF
⇒△ABC≅△DEF by SSS congruence.
Hence proved.