Quadrilateral Proofs Worksheet

Grade 12 Math worksheet focusing on proving properties of various quadrilaterals including parallelograms, rectangles, rhombuses, and squares.

Grade 12 Math GeometryQuadrilateral Proofs

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Includes

3 Short AnswerTrue / FalseFill in the BlanksMultiple Choice

Standards

CCSS.MATH.CONTENT.HSG.CO.C.10CCSS.MATH.CONTENT.HSG.SRT.B.5

Topics

MathGeometryQuadrilateralsProofsGrade 12

8 sections · Free to use · Printable

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.