Question

what are the corresponding parts of the figures below? select all that apply.

Explanation:

Step1: Analyze Side Lengths

• \( \overline{LM} \) has length 8 cm, \( \overline{SR} \) has length 8 cm. So \( \overline{LM} \cong \overline{SR} \) (correct).
• \( \overline{NM} \): Let's check the other figure. \( \overline{RS} \) is 8 cm, but \( \overline{NM} \) is part of the first quadrilateral. Wait, actually, \( \overline{NM} \) length: Wait, the first quadrilateral \( LMKN \)? Wait, \( \overline{LM} = 8 \), \( \overline{LK}=12 \), \( \overline{KN}=19 \), \( \overline{NM}=21 \). The second quadrilateral \( SRQT \): \( \overline{SR}=8 \), \( \overline{ST}=12 \), \( \overline{TQ}=19 \), \( \overline{QR}=21 \). Wait, so \( \overline{NM} \) (21 cm) should correspond to \( \overline{QR} \) (21 cm), not \( \overline{RS} \) (8 cm). So \( \overline{NM} \cong \overline{RS} \) is wrong.

Step2: Analyze Angles

• \( \angle L \): In first quadrilateral, \( \angle L \) has two arcs. \( \angle S \) in second quadrilateral has two arcs. So \( \angle L \cong \angle S \) (correct).
• \( \angle L \) and \( \angle T \): \( \angle T \) has one arc? Wait, no, looking at the arcs: \( \angle L \) has two arcs, \( \angle K \) has three arcs, \( \angle N \) has one arc, \( \angle M \) has one arc? Wait, no, the first quadrilateral: \( \angle L \) (two arcs), \( \angle K \) (three arcs), \( \angle N \) (one arc), \( \angle M \) (one arc). Second quadrilateral: \( \angle R \) (one arc), \( \angle S \) (two arcs), \( \angle T \) (three arcs), \( \angle Q \) (one arc). So \( \angle L \) (two arcs) corresponds to \( \angle S \) (two arcs), \( \angle K \) (three arcs) corresponds to \( \angle T \) (three arcs), \( \angle N \) (one arc) corresponds to \( \angle Q \) (one arc), \( \angle M \) (one arc) corresponds to \( \angle R \) (one arc). So \( \angle L \cong \angle T \) is wrong (since \( \angle T \) has three arcs, \( \angle L \) has two).

So correct corresponding parts:

• \( \overline{LM} \cong \overline{SR} \) (correct)
• \( \angle L \cong \angle S \) (correct)

Wrong ones: \( \overline{NM} \cong \overline{RS} \), \( \angle L \cong \angle T \)

Answer:

Correct options:

• \( \overline{LM} \cong \overline{SR} \)
• \( \angle L \cong \angle S \)

(So the initially checked wrong ones: \( \overline{NM} \cong \overline{RS} \) and \( \angle L \cong \angle T \) should be unchecked, and \( \overline{LM} \cong \overline{SR} \) and \( \angle L \cong \angle S \) are correct.)