Given: RT ≅ TV and ST ≅ TU Prove: RSVU is a parallelogram. Statements Reasons 1. RT ≅ TV; ST ≅ TU 1. given 2. ∠RTS and ∠VTU are vert. ∠s; ∠RTU and ∠VTS are vert. ∠s 2. definition of vertical angles 3. ∠RTS ≅ ∠VTU; ∠RTU ≅ ∠VTS 3. vertical angles are congruent 4. ? 4. SAS congruency theorem 5. ∠VRS ≅ ∠RVU; ∠USR ≅ ∠SUV; ∠VRU ≅ ∠RVS; ∠RUS ≅ ∠USV 5. CPCTC 6. ∠VRS and ∠RVU, ∠USR and ∠SUV, ∠VRU and ∠RVS, ∠RUS and ∠USV are each a pair of alternate interior angles 6. definition of alternate interior angles 7. RS ∥ UV and RU ∥ SV 7. converse of the parallelogram diagonal theorem 8. RSVU is a parallelogram 8. definition of parallelogram What is the missing statement in step 4?

It is a polygon that has four sides and four corners. The sum of the internal angle is 360 degrees. In a parallelogram, pairs of opposite sides are parallel and equal.

Given

RT ≅ TV and ST ≅ TU

Prove

RSVU is a parallelogram.

How to prove?

Let RSVU is quadrilateral.

1. RT ≅ TU and ST ≅ TU, means half of the diagonal.

2. ∠RTS and ∠VTU are vertically opposite angles, ∠RTU and ∠VTS are vertically opposite angles.

3. ∠RTS and ∠VTU are vertically opposite angles, ∠RTU and ∠VTS are vertically opposite angles.

4. Then according to Side, angle, and side theorem it is clear that both triangles are congruent to each other.

5. ∠VRS ≅ ∠RVU are alternate angles, ∠USR ≅ ∠SUV are alternate angles, ∠VRU ≅ ∠RVS are alternate angles, ∠RUS ≅ ∠USV are alternate angles.

6. When two lines are parallel to each other then a line is passing through these lines then it will make alternate angles.

7. Converse of the parallelogram diagonal theorem

8. RSVU is a parallelogram.

More about the parallelogram link is given below.

https://brainly.com/question/1563728