Question

congruent figures
given polygons table ≅ frown. which of the following is not true?
o ab ≅ ro
o eb ≅ ow
o ∠ate ≅ ∠rfn
o ∠tab ≅ ∠orf

Explanation:

Step1: Analyze the correspondence of congruent polygons

When two polygons are congruent, their corresponding sides and angles are congruent. For \(TABLE\cong FROWN\), the correspondence is \(T - F\), \(A - R\), \(B - O\), \(L - W\), \(E - N\).

Step2: Check each option

• For \(\overline{AB}\cong\overline{RO}\): Since \(A - R\) and \(B - O\), \(\overline{AB}\) corresponds to \(\overline{RO}\), so \(\overline{AB}\cong\overline{RO}\) is True.
• For \(\overline{EB}\cong\overline{OW}\): Since \(E - N\) and \(B - O\), \(\overline{EB}\) does not correspond to \(\overline{OW}\). The correct correspondence for \(\overline{EB}\) is \(\overline{NO}\) (because \(E - N\) and \(B - O\)).
• For \(\angle ATE\cong\angle RFN\): Since \(A - R\), \(T - F\), \(E - N\), \(\angle ATE\) corresponds to \(\angle RFN\), so \(\angle ATE\cong\angle RFN\) is True.
• For \(\angle TAB\cong\angle ORF\): Since \(T - F\), \(A - R\), \(B - O\) (re - arranging the order of vertices for angle correspondence, \(\angle TAB\) corresponds to \(\angle ORF\) (because in congruent polygons, angle correspondence follows the vertex - to - vertex correspondence), so \(\angle TAB\cong\angle ORF\) is True.

Answer:

\(\overline{EB}\cong\overline{OW}\)