Question

what are the corresponding parts of the figures below? select all that apply.
figures: left quadrilateral with vertices m, l, k, n (ml=14 mi, lk=18 mi, kn=29 mi, nm=34 mi; angles: ∠m=85°, ∠l=129°, ∠k=93°, ∠n=53°). right quadrilateral with vertices v, u, t, s (vu=18 mi, ut=14 mi, ts=34 mi, sv=29 mi; angles: ∠v=93°, ∠u=129°, ∠t=85°, ∠s=53°). options: ∠l ≅ ∠u (checked), ∠m ≅ ∠t (checked), ( overline{ml} cong overline{tu} ) (checked), ∠n ≅ ∠s (checked)

Explanation:

To determine corresponding parts, we analyze angles and sides:

Step1: Analyze ∠L and ∠U

∠L is \(129^\circ\), ∠U is \(129^\circ\). So \( \angle L \cong \angle U \).

Step2: Analyze ∠M and ∠T

∠M is \(85^\circ\), ∠T is \(85^\circ\). So \( \angle M \cong \angle T \).

Step3: Analyze \( \overline{ML} \) and \( \overline{TU} \)

\( \overline{ML} = 14 \) mi, \( \overline{TU} = 14 \) mi. So \( \overline{ML} \cong \overline{TU} \).

Step4: Analyze ∠N and ∠S

∠N is \(53^\circ\), ∠S is \(53^\circ\). So \( \angle N \cong \angle S \).

Answer:

\( \angle L \cong \angle U \), \( \angle M \cong \angle T \), \( \overline{ML} \cong \overline{TU} \), \( \angle N \cong \angle S \) (all the selected options are correct as per angle measures and side lengths matching).