Parallelogram Proofs Worksheet
A Grade 10 Math worksheet focused on proving properties of parallelograms and using theorems to solve problems.
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Parallelogram Proofs Worksheet
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Read each question carefully and provide clear, logical proofs or answers. Show all your work for full credit.
1. Consider parallelogram ABCD. If the measure of angle A is 70 degrees, what are the measures of angles B, C, and D?
2. In parallelogram PQRS, diagonal PR and QS intersect at point T. If PT = 5 cm and QT = 8 cm, what are the lengths of PR and QS?
3. A quadrilateral is a parallelogram if both pairs of sides are parallel.
4. If the diagonals of a quadrilateral each other, then the quadrilateral is a parallelogram.
5. A quadrilateral is a parallelogram if one pair of opposite sides is both and parallel.
6. All rectangles are parallelograms.
True
False
7. If a quadrilateral has four right angles, 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.
9. Given: Parallelogram FGHI. Prove: Opposite angles are congruent (∠F ≅ ∠H and ∠G ≅ ∠I).
10. Which of the following conditions is NOT sufficient to prove that a quadrilateral is a parallelogram?
Both pairs of opposite sides are congruent.
Both pairs of opposite angles are congruent.
The diagonals are congruent.
One pair of opposite sides is both parallel and congruent.