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

Ask by Savage Frank. in the United States
Jan 30,2025

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Answer

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

Solution

The correct corresponding pair is: **\( \overline{S T} \cong \overline{W V} \)** **Explanation:** In the congruent triangles \( \triangle T R S \cong \triangle V X W \), the correspondence of vertices is as follows: - \( T \) corresponds to \( V \), - \( R \) corresponds to \( X \), - \( S \) corresponds to \( W \). Therefore, the side \( \overline{S T} \) in \( \triangle T R S \) corresponds to the side \( \overline{W V} \) in \( \triangle V X W \). **Answer:** \( \overline{S T} \cong \overline{W V} \)

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Since \( \triangle T R S \cong \triangle V X W \), it follows that corresponding sides and angles are congruent. This means that each side in triangle TRS matches with a side in triangle V X W in a specific order. For example, if we denote the vertices as follows: \( T \) corresponds to \( V \), \( R \) corresponds to \( X \), and \( S \) corresponds to \( W \). Thus, we can conclude: - \( \overline{ST} \) corresponds to \( \overline{WX} \), - \( \overline{RS} \) corresponds to \( \overline{XV} \), - \( \angle T \) corresponds to \( \angle V \), - \( \overline{TR} \) corresponds to \( \overline{VW} \). Out of your provided options, the pair \( \angle T \cong \angle W \) is incorrect because \( \angle T \) should correspond to \( \angle V \). Therefore, none of the pairs provided correspond correctly based on the triangle congruence. In a nutshell, remember the order of the vertices matters significantly in congruence - it’s like a secret handshake among triangles! Knowing how to precisely match angles and sides can be the key to solving various geometric puzzles. And if you mix it up? Well, it’s like trying to match socks while blindfolded! Keep your corresponding pairs in line and you'll ace those triangle problems in no time!

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