Proofs with Parallelograms Worksheet
A Grade 9 Geometry worksheet focusing on understanding and proving properties of parallelograms and their special cases.
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Proofs with Parallelograms
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Read each question carefully and provide a complete proof or answer as required. Show all your work for full credit.
1. What are the five main properties of a parallelogram? List them below.
2. Which of the following conditions guarantees that a quadrilateral is a parallelogram?
Diagonals are congruent.
One pair of opposite sides is parallel and congruent.
Consecutive angles are congruent.
All four sides are congruent.
3. If a quadrilateral has diagonals that bisect each other, then it is a .
4. In a parallelogram, opposite sides are and .
5. Given parallelogram ABCD with diagonals AC and BD intersecting at E. Prove that triangle ABE is congruent to triangle CDE.
6. A quadrilateral with four right angles is always a parallelogram.
True
False
7. If a quadrilateral has congruent diagonals, it must be a parallelogram.
True
False
8. Graph the points A(1,1), B(4,1), C(5,3), and D(2,3). Prove that quadrilateral ABCD is a parallelogram using the distance formula.
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