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