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Special Quadrilaterals

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Explore the properties and relationships of special quadrilaterals through true/false statements. This engaging exercise tests knowledge on squares, rhombuses, rectangles, and kites, including their diagonals and angles. Learn that a square is indeed a rhombus, but not all rhombuses are rectangles, and understand the conditions for parallelograms and trapezoids to be isosceles or otherwise. This study simplifies complex geometric concepts while enhancing critical thinking skills necessary for honors geometry.

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Special Quadrilaterals

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  1. Special Quadrilaterals Honors Geometry

  2. True/False Every square is a rhombus.

  3. TRUE – four congruent sides

  4. True/False If the diagonals of a quadrilateral are perpendicular, then it is a rhombus.

  5. False – diagonals don’t have to be congruent or bisect each other.

  6. True/False The diagonals of a rectangle bisect its angles.

  7. FALSE (draw an EXTREME rectangle!)

  8. True/False A kite with all consecutive angles congruent must be a square.

  9. TRUE

  10. True/False Diagonals of trapezoids are congruent.

  11. FALSE – not always!

  12. True/False A parallelogram with congruent diagonals must be a rectangle.

  13. TRUE

  14. True/False Some rhombuses are rectangles.

  15. True – some rhombuses also have right angles

  16. True/False The diagonals of a rhombus are congruent.

  17. False – not always!

  18. True/False If the diagonals of a parallelogram are perpendicular, it must be a rhombus.

  19. TRUE

  20. True/False Diagonals of a parallelogram bisect the angles.

  21. FALSE

  22. True/False A quadrilateral that has diagonals that bisect and are perpendicular must be a square.

  23. FALSE (could be rhombus… right angles not guaranteed)

  24. Sometimes/Always/Never A kite with congruent diagonals is a square.

  25. FALSE – could be, but diagonals don’t have to bisect each other.

  26. Give the most descriptive name: A parallelogram with a right angle must be what kind of shape?

  27. Rectangle

  28. Give the most descriptive name: A rectangle with perpendicular diagonals must be what kind of shape?

  29. SQUARE

  30. Give the most descriptive name A rhombus with consecutive angles congruent must be a:

  31. SQUARE

  32. Give the most descriptive name: A parallelogram with diagonals that bisect its angles must be a:

  33. Rhombus

  34. Proving that a Quad is a Rectangle • If a parallelogram contains at least one right angle, then it is a rectangle. • If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. • If all four angles of a quadrilateral are right angles, then it is a rectangle.

  35. Proving that a Quad is a Kite • If two disjoint pairs of consecutive sides of a quadrilateral are congruent, then it is a kite. • If one of the diagonals of a quadrilateral is the perpendicular bisector of the other diagonal, then it is a kite.

  36. Proving that a Quad is a Rhombus • If a parallelogram contains a pair of consecutive sides that are congruent, then it is a rhombus. • If either diagonal of a parallelogram bisects two angles of the parallelogram, then it is a rhombus. • If the diagonals of a quadrilateral are perpendicular bisectors of each other, then the quadrilateral is a rhombus.

  37. Proving that a Quad is a Square • If a quadrilateral is both a rectangle and a rhombus, then it is a square.

  38. Proving that a Trapezoid is Isosceles • If the non-parallel sides of a trapezoid are congruent, then it is isosceles. • If the lower or upper base angles of a trapezoid are congruent, then it is isosceles. • If the diagonals of a trapezoid are congruent, then it is isosceles.

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