Question
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iven \( \triangle T R S \cong \triangle V X W \), which of the following corresponding pairs is correct (1 point) \( \overline{S T} \cong \overline{W V} \) \( \overline{R S} \cong \overline{V X} \) \( \overline{\angle T \cong \angle W} \) \( \overline{T R} \cong \overline{X W} \)

Ask by Pierce Sanders. in the United States
Jan 30,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

\( \overline{S T} \cong \overline{W V} \)

Solution

Given that \( \triangle T R S \cong \triangle V X W \), the correspondence between the vertices is as follows: - \( T \) corresponds to \( V \) - \( R \) corresponds to \( X \) - \( S \) corresponds to \( W \) Using this correspondence: 1. \( \overline{S T} \) should correspond to \( \overline{W V} \), which is correct. 2. \( \overline{R S} \) should correspond to \( \overline{X W} \), not \( \overline{V X} \). 3. \( \angle T \) should correspond to \( \angle V \), not \( \angle W \). 4. \( \overline{T R} \) should correspond to \( \overline{V X} \), not \( \overline{X W} \). Thus, the correct corresponding pair is: \( \overline{S T} \cong \overline{W V} \) **Answer:** \( \overline{S T} \cong \overline{W V} \)

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Bonus Knowledge

In congruent triangles, corresponding sides and angles are equal, so the pairs must align based on their positions in each triangle. In the case of \( \triangle T R S \cong \triangle V X W \), we can identify that \( \overline{S T} \) corresponds with \( \overline{W V} \), while \( \overline{R S} \) corresponds with \( \overline{V X} \). Looking more closely at those options, \( \overline{S T} \cong \overline{W V} \) is indeed correct as S corresponds to W and T corresponds to V in the structures of the triangles. This shows the beauty of geometry where shapes maintain their integrity through transformation!

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