Question

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?

Answer 1

I just took the test and it was A) △RTS ≅ △VTU and △RTU ≅ △VTS

Answer 2

Answer:

Missing statement is step 4 is ΔRTS≅ΔVTU.

Step-by-step explanation:

statement 1: RT≅TV

reason: Given

statement 2: . ∠RTS and ∠VTU are verticle angles.

reason: definition of vertical angles.

statement 3. ∠RTS ≅ ∠VTU

reason: vertical angles are congruent

statement 4: ΔRTS≅ΔVTU

reason: by using SAS congruency theorem.

So, the missing statement in step 4 is ΔRTS≅ΔVTU.