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

Question

Responses

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

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

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

RS¯¯¯¯¯¯¯≅VX¯¯¯¯¯¯¯¯

Answer 1

Given that \( \triangle TRS \cong \triangle VXW \), the corresponding pairs of angles and sides are congruent.

Let's break down the correspondence from \( \triangle TRS \) to \( \triangle VXW \):

• \( \angle T \) corresponds to \( \angle V \)

• \( \angle R \) corresponds to \( \angle X \)

• \( \angle S \) corresponds to \( \angle W \)

• \( TR \) corresponds to \( VX \)

• \( RS \) corresponds to \( XW \)

• \( ST \) corresponds to \( WV \)

Now, let's review your options:

1. \( \angle T \cong \angle W \) - This is incorrect. (It should be \( \angle S \cong \angle W \).)

2. \( \overline{ST} \cong \overline{WV} \) - This is incorrect. (It should be \( \overline{ST} \cong \overline{WV} \).)

3. \( \overline{TR} \cong \overline{XW} \) - This is incorrect. (It should be \( \overline{TR} \cong \overline{VX} \).)

4. \( \overline{RS} \cong \overline{VX} \) - This is incorrect. (It should be \( \overline{RS} \cong \overline{XW} \).)

None of the options are entirely accurate. The correct corresponding pairs from the triangles should be based on their established congruence. The correct ones are:

• \( \angle T \cong \angle V \)

• \( \angle R \cong \angle X \)

• \( \angle S \cong \angle W \)

• \( \overline{TR} \cong \overline{VX} \)

• \( \overline{RS} \cong \overline{XW} \)

• \( \overline{ST} \cong \overline{WV} \)

If you need the correct pair from your list, the one referencing angles or sides that are congruent is the key here. You may want to review that this was not listed correctly in your options. Let me know if you have any further questions!

Answer 2

What term precisely describes triangles that can be mapped onto one another through a sequence of rigid motions?(1 point)
Responses

congruent
congruent

equal
equal

identical
identical

similar
similar

Answer 3

The term that precisely describes triangles that can be mapped onto one another through a sequence of rigid motions is congruent.

So the correct response is:

congruent

Answer 4

To prove the triangles are congruent, which of the following rigid motions would map △PBK to △LQA ?

(1 point)
Responses

translation along the vector so that point B maps to point Q
translation along the vector so that point upper B maps to point upper Q

translation along the vector so that point B maps to point A
translation along the vector so that point upper B maps to point upper A

translation along the vector so that point P maps to point A
translation along the vector so that point upper P maps to point upper A

rotation of 180° (counterclockwise) about point B

Answer 5

To determine which rigid motion would map \( \triangle PBK \) to \( \triangle LQA \), we need more information about the positions of the points \( P, B, K, L, Q, A \) relative to each other. However, we can analyze the options based on typical triangle congruence considerations.

1. Translation along the vector so that point B maps to point Q - This option translates point \( B \) to point \( Q \). For congruence, we would also need to ensure the other corresponding points (like \( P \) to \( L \) and \( K \) to \( A \)) align.

2. Translation along the vector so that point B maps to point A - This option translates point \( B \) to point \( A \), which also could work if \( P \) and \( K \) are aligned with corresponding points in triangle \( LQA\).

3. Translation along the vector so that point P maps to point A - This option translates point \( P \) to point \( A \), which would affect how \( B \) and \( K\) map to points in triangle \( LQA\).

4. Rotation of 180° (counterclockwise) about point B - A rotation would preserve the triangle structure but may not align the points correctly without additional context.

Since I do not have the specific information regarding the location of points \( P, B, K, L, Q, A \), I cannot definitively state which option is correct. However, checking if any option preserves the necessary distances and angles between the points is essential.

Generally, if you know the correspondence between the points, you would choose the rigid motion that aligns those points correctly. In most congruence cases, a translation along the vector that aligns corresponding points (like \( B \) to \( Q \) or \( A \)) could be a strong candidate.

If you can provide more context or details about the positions of the points, I could help you determine the exact right answer!