Question

what are the corresponding parts of the figures below? select all that apply. figures: left polygon with vertices m, l, k, j (angles: ∠m=77°, ∠l=149°, ∠k=84°, ∠j=50°; sides: ml=18 ft, lk=14 ft, kj=37 ft, jm=37 ft); right polygon with vertices r, q, t, s (angles: ∠r=77°, ∠q=50°, ∠t=84°, ∠s=149°; sides: rq=37 ft, qt=37 ft, ts=14 ft, sr=18 ft). options: ∠l ≅ ∠s, ∠k ≅ ∠t, ∠m ≅ ∠r, overline{kj} ≅ overline{tq}

Explanation:

Step1: Analyze ∠L and ∠S

∠L is 149° and ∠S (from the second figure, the angle at S) should be equal to ∠L as per the figure's congruency (since the angle measures match for corresponding angles). So ∠L ≅ ∠S.

Step2: Analyze ∠K and ∠T

∠K is 84° and ∠T is 84°, so their measures are equal, hence ∠K ≅ ∠T.

Step3: Analyze ∠M and ∠R

∠M is 77° and ∠R is 77°, so their measures are equal, hence ∠M ≅ ∠R.

Step4: Analyze \(\overline{KJ}\) and \(\overline{TQ}\)

\(\overline{KJ}\) has length 37 ft and \(\overline{TQ}\) has length 37 ft, so their lengths are equal, hence \(\overline{KJ} \cong \overline{TQ}\).

Answer:

The correct corresponding parts are:

• \(\boldsymbol{\angle L \cong \angle S}\)
• \(\boldsymbol{\angle K \cong \angle T}\)
• \(\boldsymbol{\angle M \cong \angle R}\)
• \(\boldsymbol{\overline{KJ} \cong \overline{TQ}}\)