Question

what are the corresponding parts of the figures below? select all that apply.
lm ≅ uv
∠m ≅ ∠v
∠k ≅ ∠t
∠n ≅ ∠w

Explanation:

Step1: Analyze the first figure's vertices and angles

The first figure has vertices \(L\), \(K\), \(N\), \(M\). Angles: at \(L\) is \(135^{\circ}\), at \(K\) is \(71^{\circ}\), at \(N\) is \(57^{\circ}\), at \(M\) is \(97^{\circ}\).

Step2: Analyze the second figure's vertices and angles

The second figure has vertices \(U\), \(V\), \(W\), \(T\). Angles: at \(U\) is \(135^{\circ}\), at \(V\) is \(97^{\circ}\), at \(W\) is \(57^{\circ}\), at \(T\) is \(71^{\circ}\).

Step3: Match corresponding angles and sides

• For angles: \(\angle M = 97^{\circ}\) and \(\angle V=97^{\circ}\), \(\angle K = 71^{\circ}\) and \(\angle T = 71^{\circ}\), \(\angle N=57^{\circ}\) and \(\angle W = 57^{\circ}\).
• For sides: \(\overline{LM}\) (length \(15\) in) corresponds to \(\overline{UT}\) (length \(8\) in) is incorrect. But \(\overline{MN}\) (length \(19\) in) corresponds to \(\overline{WV}\) (length \(19\) in) is not the pair asked. The correct side - angle correspondence:
• \(\angle M\) and \(\angle V\): \(\angle M\cong\angle V\) (both \(97^{\circ}\))
• \(\angle K\) and \(\angle T\): \(\angle K\cong\angle T\) (both \(71^{\circ}\))
• \(\angle N\) and \(\angle W\): \(\angle N\cong\angle W\) (both \(57^{\circ}\))

Answer:

\(\angle M\cong\angle V\), \(\angle K\cong\angle T\), \(\angle N\cong\angle W\)