Proofs with Parallelograms Worksheet
A Grade 12 math worksheet focusing on geometric proofs involving properties of parallelograms, including their sides, angles, and diagonals.
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Standards
Proofs with Parallelograms
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Read each question carefully and provide a complete proof or answer as required. Show all your work and justifications.
1. Given parallelogram ABCD, prove that opposite sides are congruent (AB ≅ CD and BC ≅ DA).
2. Complete the proof: The diagonals of a parallelogram bisect each other. Given parallelogram PQRS with diagonals PR and QS intersecting at T. Prove that PT ≅ RT and QT ≅ ST.
Statement: PQRS is a parallelogram. Reason: Given. Statement: PQ || SR and PS || QR. Reason: . Statement: ∠PQT ≅ ∠RST and ∠QPT ≅ ∠SRT. Reason: . Statement: PQ ≅ SR. Reason: . Statement: ΔPQT ≅ ΔRST. Reason: . Statement: PT ≅ RT and QT ≅ ST. Reason: .
3. In parallelogram WXYZ, if m∠W = (5x + 10)° and m∠Y = (7x - 20)°, what is the value of x?
5
10
15
20
4. Given quadrilateral ABCD with diagonals AC and BD. If AC and BD bisect each other, prove that ABCD is a parallelogram.
5. A quadrilateral with one pair of opposite sides parallel and congruent is always a parallelogram.
True
False