Question

Which triangles must be congruent? Given this information about ΔABC, ΔDEF, and ΔGHI:

Answer 1

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