Question

Which triangles must be congruent?

Answer 1

Δ ABC ≅ Δ FDE ≅ Δ GIH

Explanation:

Between Δ ABC and Δ FDE, given that

(i) AB = DF

(ii) BC = HI and DE = HI, hence, BC = DE

(iii) ∠ B = ∠ D

Hence, by Side-Angle -Side i.e. SAS criteria Δ ABC ≅ Δ FDE

Again, between Δ ABC and Δ GIH, given that

(i) AB = GI

(ii) BC = HI and

(iii) ∠ B = ∠ I.

Hence, by Side-Angle-Side i.e. SAS criteria Δ ABC ≅ Δ GIH.

Therefore, Δ ABC ≅ Δ FDE ≅ Δ GIH (Answer)