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Special Quadrilaterals

Explore properties of special quadrilaterals in honors geometry with true/false statements, descriptive names, and proof examples to enhance understanding. Learn about squares, rhombuses, rectangles, kites, parallelograms, and trapezoids.

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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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