Question

1. if bingo ≅ turfs which of the following congruency statements is not necessarily true?

a. \\( \overline { i n } \cong \overline { u r } \\) b. \\( \angle n g i \cong \angle u r f \\) c. \\( \overline { t s } \cong \overline { b o } \\) d. gobin ≅ fs

Explanation:

Step1: Analyze the congruent polygons

When \(BINGO\cong TURFS\), the corresponding parts (sides and angles) are congruent. The order of the letters in the congruence statement matters.

Step2: Check each option

• Option A:

In \(BINGO\) and \(TURFS\), the side \(\overline{IN}\) in \(BINGO\) corresponds to \(\overline{UR}\) in \(TURFS\) (by the order of the congruence \(BINGO\cong TURFS\)). So, \(\overline{IN}\cong\overline{UR}\) is True.

• Option B:

The angle \(\angle NGI\) in \(BINGO\) does not correspond to \(\angle URF\) in \(TURFS\). The correct correspondence for angles is based on the order of the letters in the congruence \(BINGO\cong TURFS\). For example, \(\angle B\) corresponds to \(\angle T\), \(\angle I\) corresponds to \(\angle U\), \(\angle N\) corresponds to \(\angle R\), \(\angle G\) corresponds to \(\angle F\), \(\angle O\) corresponds to \(\angle S\). So, \(\angle NGI\cong\angle URF\) is NOT True.

• Option C:

The side \(\overline{TS}\) in \(TURFS\) corresponds to \(\overline{BO}\) in \(BINGO\) (by the order of the congruence \(BINGO\cong TURFS\)). So, \(\overline{TS}\cong\overline{BO}\) is True.

• Option D:

The polygon \(GOBIN\) (a re - arrangement of the vertices of \(BINGO\)) corresponds to \(FS\) (a re - arrangement of the vertices of \(TURFS\)) in terms of congruence. Since \(BINGO\cong TURFS\), \(GOBIN\cong FS\) is True.

Answer:

B. \(\angle NGI\cong\angle URF\)