We are given four congruent sides. Let's mark them in the given diagram. We will also highlight the vertical angles ∠QRV and ∠WRS.
By the Vertical Angles Theorem we get ∠QRV ≅ ∠WRS.
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QR ≅ WR & Side
∠QRV ≅ ∠WRS & Included Angle
RV ≅ RS & Side
Using the Side-Angle-Side (SAS) Congruence Postulate we conclude that △ QRV ≅ △ WRS, which implies that ∠Q ≅ ∠W. Next, we will highlight another pair of vertical angles.
One more time, by the Vertical Angles Theorem we get ∠QRT ≅ ∠WRU.
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∠Q ≅ ∠W & Angle
QR ≅ WR & Included Side
∠QRT ≅ ∠WRU & Angle
By applying the Angle-Side-Angle (ASA) Congruence Postulate we conclude that △ QRT ≅ △ WRU, which implies that QT ≅ WU.
Two-Column Proof Table
In the following table we summarize the proof we did before.
