Quadrilateral Family Tree and Properties
Name: ___________________________________ #___
1. Quadrilateral: _____ sided polygon
2. Kite: A ________________________ with 2 pairs of adjacent congruent sides.
3. Parallelogram: A ______________________ with two pairs of opposite sides parallel.
4. Trapezoid: A ____________________________ with one pair of opposite sides parallel.
5. Rhombus: A ____________________________ with four congruent sides.
6. Rectangle: A ____________________________ with four right angles
7. Square: A _____________________________ with four congruent sides.
To the right is our quadrilateral family tree. The
properties we learned yesterday about parallelograms
also apply to anything below them (and connected to
them) in the family tree.
8. Does a trapezoid have all the properties of a
parallelogram?
9. Could a trapezoid have diagonals that bisect one
another? Explain your reasoning.
10. If a quadrilateral has one pair of opposite sides
parallel and the other pair of opposite sides congruent,
can you guarantee that it’s a parallelogram? Explain your
reasoning.
11. Does a rhombus have consecutive angles that are
supplementary? Explain your reasoning.
Think about the quadrilaterals above and their diagonals. Fill in the blank with the most general name of the
quadrilateral that is guaranteed to have these properties.
12. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a __________________________.
13. If the diagonals of a quadrilateral bisect each other and are equal in length, then the quadrilateral is a
__________________________.
14. If the diagonals of a quadrilateral are perpendicular bisectors of each other, then the quadrilateral is a
__________________________.
15. If the diagonals of a quadrilateral are the same length and perpendicular bisectors of each other, then the
quadrilateral is a __________________________.
16. If the diagonals of a quadrilateral are such that one diagonal is the perpendicular bisector of the other, then the
quadrilateral is a __________________________.
Honors: Given that quadrilateral ABCD is a rhombus, prove the diagonals are perpendicular.
College Prep: Given that quadrilateral ABCD is a rectangle, prove the diagonals are congruent.