Question

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

(figure 1: quadrilateral lmon with sides: lm=11 cm, mn=24 cm, no=19 cm, ol=15 cm; angles: ∠l=130°, ∠m=76°, ∠n=65°, ∠o=89°)

(figure 2: quadrilateral uvts with sides: uv=24 cm, vt=11 cm, ts=15 cm, su=19 cm; angles: ∠u=65°, ∠v=76°, ∠s=130°, ∠t=89°)

options (with checkmarks):
$overline{on} \cong \overline{tu}$
$overline{lo} \cong \overline{st}$
$overline{nm} \cong \overline{uv}$
$\angle n \cong \angle u$

Explanation:

Step1: Analyze \( \overline{ON} \) and \( \overline{TU} \)

Check lengths: \( ON = 19 \, \text{cm} \), \( TU = 19 \, \text{cm} \). So \( \overline{ON} \cong \overline{TU} \) (equal length, congruent segments).

Step2: Analyze \( \overline{LO} \) and \( \overline{ST} \)

Lengths: \( LO = 15 \, \text{cm} \), \( ST = 15 \, \text{cm} \). Thus \( \overline{LO} \cong \overline{ST} \).

Step3: Analyze \( \overline{NM} \) and \( \overline{UV} \)

Lengths: \( NM = 24 \, \text{cm} \), \( UV = 24 \, \text{cm} \). So \( \overline{NM} \cong \overline{UV} \).

Step4: Analyze \( \angle N \) and \( \angle U \)

Angles: \( \angle N = 65^\circ \), \( \angle U = 65^\circ \). Hence \( \angle N \cong \angle U \).

Answer:

\( \overline{ON} \cong \overline{TU} \), \( \overline{LO} \cong \overline{ST} \), \( \overline{NM} \cong \overline{UV} \), \( \angle N \cong \angle U \) (all selected options are correct as per congruence of corresponding parts in congruent figures, verified by equal lengths/angles).