Quadrilateral Proofs Worksheet
Grade 12 Math worksheet focusing on proving properties of various quadrilaterals including parallelograms, rectangles, rhombuses, and squares.
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Quadrilateral Proofs
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Read each question carefully and provide a complete proof or answer as required. Show all your work and reasoning.
1. Given a quadrilateral ABCD with diagonals AC and BD bisecting each other at point E. Prove that ABCD is a parallelogram.
2. Prove that if the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
3. Indicate whether each statement is True or False.
a) All rhombuses are squares.
True
False
b) A trapezoid always has exactly one pair of parallel sides.
True
False
4. Complete the following statements:
a) If a quadrilateral has four congruent sides, it is a .
b) The opposite angles of a parallelogram are .
c) The diagonals of a kite are .
5. Which of the following quadrilaterals always has perpendicular diagonals?
Parallelogram
Rectangle
Rhombus
Isosceles Trapezoid
6. Given a quadrilateral PQRS with four congruent sides and one right angle. Prove that PQRS is a square.