Question

Given: RW ≅ WT; UW ≅ WS Prove: RSTU is a parallelogram. Identify the steps that complete the proof.

Answer 1

Identify the steps that complete the proof.

♣ = ✔ vertical angles theorem

♦ = ✔ SAS

♠ = ✔ CPCTC

Answer 2

Answer with explanation:

Given: RW ≅ WT; UW ≅ WS

To Prove:≡ RSTU is a parallelogram.

Proof: In ΔRWU and ΔTWS

1. RW ≅ WT

2. UW ≅ WS

3. ∠RWU=∠TWS→→[Vertically opposite angles]

ΔRWU≅ΔTWS⇒⇒⇒[SAS]

RU=ST→[CPCT]

∠WRU=∠WTS⇒[C PCT]

RU║ST⇒Alternate angles are equal so lines are parallel.

⇒⇒⇒If in a Quadrilateral , diagonals bisect each other ,and one pair of opposite side is equal and parallel ,so it is a parallelogram.

∴Quadrilateral R STU is a parallelogram