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Given △TRS≅△VXW, which of the following corresponding pairs is correct?(1 point)

Responses

TR¯¯¯¯¯¯¯≅XW¯¯¯¯¯¯¯¯¯¯
Modifying above upper T upper R with bar congruent to Modifying above upper V upper W with bar

ST¯¯¯¯¯¯¯≅WV¯¯¯¯¯¯¯¯¯
Modifying above upper S upper T with bar congruent to Modifying above upper W upper V with bar

∠T≅∠W
angle upper T congruent to angle upper W

RS¯¯¯¯¯¯¯≅VX¯¯¯¯¯¯¯¯

3 answers

In a congruence statement such as \( \triangle TRS \cong \triangle VXW \), the corresponding sides and angles are congruent to each other as follows:

  • \( \overline{TR} \equiv \overline{VX} \)
  • \( \overline{RS} \equiv \overline{XW} \)
  • \( \overline{ST} \equiv \overline{WV} \)
  • \( \angle T \equiv \angle V \)
  • \( \angle R \equiv \angle X \)
  • \( \angle S \equiv \angle W \)

Given the options presented, the correct corresponding pairs are:

  1. \( \overline{TR} \equiv \overline{VX} \)
  2. \( \overline{RS} \equiv \overline{XW} \)
  3. \( \angle T \equiv \angle V \), but this option is not explicitly listed.
  4. \( \overline{ST} \equiv \overline{WV} \) - This is also not correct based on the labels.

Based on the options you provided, "TR≅XW" (or rather, "TR≅VX") is indeed a congruent pair.

To summarize the choices:

  • \( \overline{TR} \equiv \overline{VX} \) (Correct)
  • \( \overline{ST} \equiv \overline{WV} \) (Incorrect)
  • \( \angle T \equiv \angle W \) (Incorrect)
  • \( \overline{RS} \equiv \overline{XW} \) (Correct)

So, the correct paired correspondence from the options is:

  • \( TR \equiv VX \)
  • \( RS \equiv XW \)

Note that angle correspondences based on \( \triangle TRS \cong \triangle VXW \) would relate angles as follows:

  • \( \angle T \equiv \angle V \)
  • \( \angle R \equiv \angle X \)
  • \( \angle S \equiv \angle W \)

You should verify the correct designation of vertices before selecting your final answer for any provided options. In the context, the following pair is correct:

  • \( \overline{TR} \equiv \overline{VX} \) (If this choice also appears, select that).
TR≅XW
these are the optio s
ST≅WV

∠T≅∠W

RS≅VX

Given the congruence \( \triangle TRS \cong \triangle VXW \), let's identify the correct corresponding pairs based on the order of the vertices:

  1. \( \triangle TRS \) corresponds to \( \triangle VXW \):
    • \( T \) corresponds to \( V \)
    • \( R \) corresponds to \( X \)
    • \( S \) corresponds to \( W \)

From this correspondence, we can conclude the following:

  • The sides corresponding based on the triangle congruence:
    • \( \overline{TR} \) corresponds to \( \overline{VX} \)
    • \( \overline{RS} \) corresponds to \( \overline{XW} \)
    • \( \overline{ST} \) corresponds to \( \overline{WV} \)

And the angles:

  • \( \angle T \) corresponds to \( \angle V \)
  • \( \angle R \) corresponds to \( \angle X \)
  • \( \angle S \) corresponds to \( \angle W \)

Now, evaluating the options you provided:

  1. \( TR \equiv XW \) - Incorrect (It should be \( TR \equiv VX \)).
  2. \( ST \equiv WV \) - Incorrect (It should be \( ST \equiv WV \)).
  3. \( \angle T \equiv \angle W \) - Incorrect (It should be \( \angle T \equiv \angle V \)).
  4. \( RS \equiv VX \) - Incorrect (It should be \( RS \equiv XW \)).

The corresponding sides and angles must match according to the initial order of vertices in the congruence statement. Based on the correct correspondences \( \triangle TRS \cong \triangle VXW \):

  • Correct pairs:
    • \( \overline{TR} \equiv \overline{VX} \)
    • \( \overline{RS} \equiv \overline{XW} \)
    • \( \overline{ST} \equiv \overline{WV} \)
    • \( \angle T \equiv \angle V \)
    • \( \angle R \equiv \angle X \)
    • \( \angle S \equiv \angle W \)

In your options, none of the provided pairs are correct based on the congruence stated above.

If you need to choose a single option:

  • None of the chosen pairs from your list are correct based on the congruence \( \triangle TRS \cong \triangle VXW \).

Please verify if there are any updates or different configurations.