Question

what are the corresponding parts of the figures below? select all that apply.
∠j ≅ ∠w
∠k ≅ ∠u
\overline{jk} ≅ \overline{uw}
\overline{ik} ≅ \overline{wu}

Explanation:

Step1: Identify corresponding angles

In congruent or similar figures (assuming these are congruent as per the markings), angles that are in the same relative position are corresponding. For the first triangle \( \triangle XYZ\) (assuming vertices \(X,Y,Z\)) and second \( \triangle VWU\) (assuming vertices \(V,W,U\)), \(\angle J\) (assuming \(J = \angle Y\)) and \(\angle W\) are not corresponding. \(\angle K\) (assuming \(K=\angle X\)) and \(\angle U\) are not corresponding.

Step2: Identify corresponding sides

For sides, \(\overline{JK}\) (assuming \(J,Y;K,X\)) and \(\overline{UW}\) (assuming \(U,W\)) are not corresponding. \(\overline{IK}\) (assuming \(I,Z;K,X\)) and \(\overline{WU}\) (assuming \(W,U\)) are not corresponding. Wait, re - evaluating:
If we assume the first triangle has vertices \(X\) (with angle \(44^{\circ}\)), \(Y\) (with angle \(22^{\circ}\)), \(Z\) (with angle \(114^{\circ}\)) and sides \(17\) in, \(42\) in, \(32\) in. The second triangle has vertices \(V\) (with angle \(22^{\circ}\)), \(W\) (with angle \(114^{\circ}\)), \(U\) (with angle \(44^{\circ}\)) and sides \(17\) in, \(42\) in, \(32\) in.
By the order of angles and sides:

• \(\angle J\) (assuming \(J\) is the \(22^{\circ}\) angle in first triangle) and \(\angle V\) ( \(22^{\circ}\) angle in second triangle) are corresponding. But if we consider the given options:

If we assume the first triangle is \(\triangle XYZ\) (with \(X\) having \(44^{\circ}\), \(Y\) having \(22^{\circ}\), \(Z\) having \(114^{\circ}\)) and second \(\triangle VWU\) ( \(V\) has \(22^{\circ}\), \(W\) has \(114^{\circ}\), \(U\) has \(44^{\circ}\))

• \(\angle J=\angle V\) (if \(J = 22^{\circ}\) angle), \(\angle K=\angle U\) (if \(K = 44^{\circ}\) angle), \(\overline{JK}=\overline{VU}\), \(\overline{IK}=\overline{WU}\) (assuming proper vertex - side mapping)

Answer:

\(\angle J\cong\angle V\), \(\angle K\cong\angle U\), \(\overline{JK}\cong\overline{VU}\), \(\overline{IK}\cong\overline{WU}\)