Question

complete the congruence statement. mnop ≅

Explanation:

Step1: Identify corresponding vertices

In congruent polygons, corresponding vertices are matched based on side - length and angle - measure.
For polygon \(MNOP\) and \(TSUV\):

• \(\angle M = 127^{\circ}\), \(\angle T=53^{\circ}\), \(\angle N = 53^{\circ}\), \(\angle S = 127^{\circ}\), \(\angle O=127^{\circ}\), \(\angle U = 127^{\circ}\), \(\angle P = 53^{\circ}\), \(\angle V=53^{\circ}\)
• Side \(MN = 30\mathrm{km}\), \(TS = 30\mathrm{km}\), \(NO = 30\mathrm{km}\), \(SU = 30\mathrm{km}\), \(OP = 30\mathrm{km}\), \(UV = 30\mathrm{km}\), \(PM = 30\mathrm{km}\), \(VT = 30\mathrm{km}\)

We can see that \(M\) corresponds to \(S\), \(N\) corresponds to \(T\), \(O\) corresponds to \(U\), \(P\) corresponds to \(V\)

Step2: Write the congruence statement

The congruence statement for polygons is written by listing the corresponding vertices in order.
So, \(MNOP\cong S T U V\)

Answer:

\(STUV\)