Question

What additional information is required to know that the triangles are congruent by ASA?

A) ∠F ≅ ∠Y

B) ∠FDE ≅ ∠YDE

C) EF ≅EY

D) EF ≅EY or FD ≅YD

Answer 1

The additional information require to know that the triangles are congruent by ASA is the option B)

B) ∠FDE ≅ ∠YDE

Explanation:

Given:

∠ DEY ≅ ∠FED

To Prove:

Δ DEY ≅ Δ DEF

Proof:

In Δ DEF and Δ DEY

∠ FED ≅ ∠DEY ……….{Given}

DE ≅ DE ……….{Reflexive Property}

∠ FDE ≅ ∠ YDE ...……..{Additional Information}

Δ DEF ≅ Δ DEY ….{ By Angle-Side-Angle test}

The additional information require to know that the triangles are congruent by ASA is the option B)

B) ∠FDE ≅ ∠YDE