Answer:
Only one pair of triangle is congruent.i., ΔABC ≅ ΔGHI
Step-by-step explanation:
Given: ΔABC , ΔDEF , ΔGHI
AB = DF , AB = GI , BC = HI , DE = HI , ∠B = ∠D = ∠I
To find: Two Congruent traingles.
We check all cases of possible congreuent triangle with given information.
1). In ΔABC and ΔDEF
AB = DF ( given )
∠B = ∠D ( given )
⇒ ΔABC and ΔDEF are not congruent as sufficient information is not given i.e., either a pair of side (BC=DE) or a pair of angle( ∠A=∠F).
2). In ΔDEF and ΔGHI
DE = HI ( given )
∠D = ∠I ( given )
⇒ ΔDEF and ΔGHI are not congruent as sufficient information is not given.i.e., either a pair of side(DF=IG) or a pair of angle(∠E=∠H).
3). In ΔABC and ΔGHI
AB = GI ( given )
BC = HI ( given )
∠B = ∠I ( given )
⇒ ΔABC ≅ ΔGHI by SAS ( Side-Angle-Side) congruence rule
Therefore, Only one pair of triangle is congruent.i., ΔABC ≅ ΔGHI
