Question
Ben uses a compass and a straightedge to construct ∠DEF ≅ ∠ABC, as shown below:
The art shows two figures. The figure on the left shows two rays BA and BC with a common endpoint B. An arc drawn from B cuts the ray BA at H and the ray BC at I. The figure on the right shows two rays ED and EF with a common endpoint E. An arc drawn from E cuts the ray ED at J and the ray EF at K. Another arc drawn from K cuts the ray ED at J.
Which statement best explains why Ben uses the width BI to create the arc JK from point E?
∠DEF ≅ ∠ABC when BH = EK, BI = JK, and HI = EJ.
BI = JK when ∠DEF ≅ ∠ABC.
BI = EJ when ∠DEF ≅ ∠ABC.
∠DEF ≅ ∠ABC when BH = EJ, BI = EK, and HI = JK.
Answers
GPT-4o mini
The best statement that explains why Ben uses the width \( BI \) to create the arc \( JK \) from point \( E \) is:
**\( \angle DEF \cong \angle ABC \) when \( BH = EK \), \( BI = JK \), and \( HI = EJ \).**
This statement directly relates the construction steps, indicating that by maintaining the same lengths \( BH \) and \( EK \) (from the original angle) and then ensuring that \( BI \) is equal to \( JK \) (the corresponding arc created), the congruence of the angles is preserved. This reflects the principles of geometric construction where segment lengths and arcs are transferred to ensure angle congruence.
**\( \angle DEF \cong \angle ABC \) when \( BH = EK \), \( BI = JK \), and \( HI = EJ \).**
This statement directly relates the construction steps, indicating that by maintaining the same lengths \( BH \) and \( EK \) (from the original angle) and then ensuring that \( BI \) is equal to \( JK \) (the corresponding arc created), the congruence of the angles is preserved. This reflects the principles of geometric construction where segment lengths and arcs are transferred to ensure angle congruence.