Please help, I'm not sure if I'm right.

To prove the QRST is a parallelogram.

Step 1: Given and

Step 2: are alternate interior angles.

Definition of alternate interior angles

Step 3: Alternate interior angle theorem:

If two parallel lines cut by a transversal then the alternate interior angles are congruence.

QR and TS are parallel lines cut by QS.

Therefore,

Step 4: Reflexive property of congruence:

Any geometric figure is congruence to itself.

Therefore,

Step 5: By the above steps

(Angle), (Angle) and (Side)

Hence (by ASA congruence theorem)

Step 6: Corresponding parts of congruence triangles are congruent.

Step 7: Property of parallelogram:

If one pair of opposite sides are both parallel and congruent, then the quadrilateral is a parallelogram.

Hence Quadrilateral QRST is a parallelogram.

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step-by-step explanation:

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