Parallelogram Proofs Worksheet

This worksheet focuses on proving properties of parallelograms and identifying parallelograms based on given conditions, suitable for Grade 12 Geometry students.

Grade 12 Math GeometryParallelogram Proofs

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Includes

2 Short AnswerFill in the BlanksMultiple ChoiceTrue / False

Standards

CCSS.MATH.CONTENT.HSG.CO.C.11CCSS.MATH.CONTENT.HSG.SRT.B.5

Topics

parallelogramproofsgeometrygrade 12math

7 sections · Free to use · Printable

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Parallelogram Proofs

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Read each question carefully and provide clear, logical proofs or answers. Show all your work.

1. Given: Quadrilateral ABCD with AB || DC and AD || BC. Prove: ABCD is a parallelogram.

2. In a parallelogram, opposite sides are and .

3. In a parallelogram, opposite angles are .

4. In a parallelogram, consecutive angles are .

5. The diagonals of a parallelogram each other.

6. Which of the following conditions is NOT sufficient to prove that a quadrilateral is a parallelogram?

Both pairs of opposite sides are parallel.

Both pairs of opposite sides are congruent.

Both pairs of opposite angles are congruent.

One pair of opposite sides is congruent.

7. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

True

False

8. If a quadrilateral has one pair of opposite sides parallel and congruent, then it is a parallelogram.

True

False

9. Given: Parallelogram PQRS with diagonals PR and QS intersecting at T. Prove: Triangle PQT is congruent to Triangle RST.