Question

question 15 (multiple choice worth 4 points) (04 02r mc) ben uses a compass and a straightedge to construct ∠def ≅ ∠abc, as shown below. 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.

Explanation:

Step1: Recall congruent - angle construction

When constructing an angle congruent to another using a compass and straight - edge, we use the SSS (Side - Side - Side) congruence criterion for triangles formed during the construction. In the construction of $\angle DEF\cong\angle ABC$, we create two triangles $\triangle BHI$ and $\triangle EJK$.

Step2: Identify corresponding sides

For $\triangle BHI$ and $\triangle EJK$ to be congruent (so that $\angle DEF\cong\angle ABC$), we need $BH = EJ$, $BI=EK$, and $HI = JK$. Ben uses the width $BI$ to create the arc $JK$ from point $E$ because when $BI = EK$, along with other corresponding equal sides, the two triangles formed during the angle - construction process will be congruent by SSS, and thus $\angle DEF\cong\angle ABC$.

Answer:

$\angle DEF\cong\angle ABC$ when $BH = EJ$, $BI = EK$, and $HI = JK$