Grade 9 Quadrilateral Proofs Worksheet
This worksheet focuses on proving properties of quadrilaterals including parallelograms, rectangles, rhombuses, and squares for Grade 9 Math students.
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Grade 9 Quadrilateral Proofs
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Read each question carefully and provide clear, logical proofs for each statement. Show all your work.
1. Given quadrilateral ABCD with diagonals AC and BD bisecting each other at point E. Prove that ABCD is a parallelogram.
2. Complete the following proof for a rectangle: Given: ABCD is a parallelogram with AC = BD. Prove: ABCD is a rectangle. Since ABCD is a parallelogram, opposite sides are and . Also, its diagonals are . Since AC = BD (given), the diagonals are . A parallelogram with congruent diagonals is a .
3. True or False: If the diagonals of a quadrilateral are perpendicular bisectors of each other, then the quadrilateral is a rhombus.
True
False
4. Given quadrilateral PQRS with PQRS being a parallelogram and PQ ≅ QR. Prove that PQRS is a rhombus.
5. Which of the following is NOT a property that guarantees a parallelogram is a square?
Its diagonals are congruent.
Its diagonals are perpendicular.
Its diagonals bisect each other.
It has four right angles and four congruent sides.