Question

if ijkl ≅ pqrs, what are the corresponding parts? select all that apply. ∠i ≅ ∠p, overline{jk} ≅ overline{qr}, ∠j ≅ ∠r, overline{ji} ≅ overline{rq}

Explanation:

When two polygons are congruent (denoted by $\cong$), their corresponding vertices, angles, and sides are congruent. The order of the letters in the congruence statement (e.g., $IJKL \cong PQRS$) tells us the correspondence: $I$ corresponds to $P$, $J$ corresponds to $Q$, $K$ corresponds to $R$, and $L$ corresponds to $S$.

• For angles: $\angle I$ (at vertex $I$) corresponds to $\angle P$ (at vertex $P$), so $\angle I \cong \angle P$ is correct. $\angle J$ should correspond to $\angle Q$ (not $\angle R$), so $\angle J \cong \angle R$ is incorrect.
• For sides: $\overline{JK}$ (between $J$ and $K$) corresponds to $\overline{QR}$ (between $Q$ and $R$), so $\overline{JK} \cong \overline{QR}$ is correct. $\overline{JI}$ (between $J$ and $I$) corresponds to $\overline{QP}$ (between $Q$ and $P$), not $\overline{RQ}$, so $\overline{JI} \cong \overline{RQ}$ is incorrect.

So the correct corresponding parts are $\angle I \cong \angle P$ and $\overline{JK} \cong \overline{QR}$.

Answer:

• $\boldsymbol{\angle I \cong \angle P}$
• $\boldsymbol{\overline{JK} \cong \overline{QR}}$