Given: Triangle SVX is congruent to triangle UTX and Line SV is parallel to line TU.

Prove: VUTS is a parallelogram.

Statement : Reason.
1. Tri SVX is congruent to Tri UTX. Reason: Given.

2. Line SV is parallel to line TU.
Reason: Given

3. Line SV is congruent to line TV.
Reason: CPOCTAC.

4. VUTS is a parallelogram.
Reason: ?

I figured all the rest of the questions out in this proof. But for number 4 I don't understand what to put. If someone would help that would be great. Thank you!

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1. Given 5. Given

2. SV // TU 6. Given
3. SV ≅ TU 7. Corresponding part of congruent
4, Given 8. Definition of parallelogram

4. Given

What is 6 ?

4. VUTS is a parallelogram.

Reason: Since triangle SVX is congruent to triangle UTX, it follows that the corresponding sides of these triangles are congruent. Therefore, line SV is congruent to line UV. Since line SV is also parallel to line TU, this implies that line TV is congruent to line UT.

Furthermore, we know that line SV is congruent to line TV (from statement 3). Therefore, we have both pairs of opposite sides of quadrilateral VUTS congruent, which is a defining property of a parallelogram. Hence, VUTS is a parallelogram.

To prove that VUTS is a parallelogram, you need to show that both pairs of opposite sides are parallel.

Here's how you can complete the proof:

5. Since Tri SVX is congruent to Tri UTX (given in statement 1), SV is congruent to UT, and SX is congruent to TX (by corresponding parts of congruent triangles).

6. From statement 3, SV is congruent to VT.

7. By the transitive property, UT is congruent to SX.

8. Since SV is parallel to TU (given in statement 2) and SV is congruent to VT (statement 6), then TU is also congruent to SX.

9. By the definition of a parallelogram, if both pairs of opposite sides are congruent, VUTS must be a parallelogram.

Therefore, VUTS is a parallelogram (statement 4) because both pairs of opposite sides, UT and SX, as well as SV and VT, are congruent and parallel.

proof