Parallelogram Proofs Worksheet
This worksheet focuses on proving properties of parallelograms and identifying parallelograms based on given conditions for Grade 9 Geometry students.
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Parallelogram Proofs
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Read each question carefully and provide a complete answer. Show all your work for proofs. Diagrams are not to scale unless specified.
1. In parallelogram ABCD, if AB = 10 cm and BC = 7 cm, what are the lengths of CD and DA?
2. In parallelogram PQRS, if m∠P = 70°, what are the measures of angles Q, R, and S?
3. Which of the following conditions guarantees that a quadrilateral is a parallelogram?
Diagonals are congruent
One pair of opposite sides is parallel and congruent
All four angles are right angles
Consecutive angles are congruent
4. If a quadrilateral has opposite sides that are parallel, then it is a .
5. The diagonals of a parallelogram bisect each .
6. A quadrilateral with two pairs of congruent opposite sides is always a parallelogram.
True
False
7. If the diagonals of a quadrilateral are perpendicular, then it is a parallelogram.
True
False
8. Given: Quadrilateral ABCD with diagonals AC and BD bisecting each other at point E.
Prove: ABCD is a parallelogram.