Special Quadrilaterals Practice Honors Geometry

Give the most descriptive name A parallelogram with perpendicular diagonals must be a: ______________

Answer Rhombus (Parallelogram diagonals must bisect each other. Diagonals don’t have to be congruent, but are perpendicular. Forms 4 congruent triangles (SAS), so 4 congruent sides.)

Give the most descriptive name A parallelogram with congruent diagonals must be a ______________________

Answer Rectangle

Give the most descriptive name A quadrilateral with perpendicular diagonals must be a: _______________

Answer Quadrilateral (Diagonals don’t have to bisect each other or be perpendicular!)

Give the most descriptive name A kite with congruent diagonals must be a: ____________________

Answer Kite – could be square, but given doesn’t say diagonals have to bisect each other! Could be:

Give the most descriptive name A parallelogram with diagonals bisecting opposite angles must be a: ___________

Answer Rhombus (Opp. angles of parallelogram are congruent, so halves of angles are congruent, forming isos. triangles with congruent sides. Opp. sides of parallelograms are congruent, so all 4 sides must be congruent.

Give the most descriptive name A rhombus with congruent diagonals must be a: ___________________

Answer Square (A parallelogram with congruent diagonals must be a rectangle, which has 4 rt. angles. A rhombus has 4 congruent sides. A shape with 4 congruent sides and angles is a square!)

Give the most descriptive name:

Answer Parallelogram (Diagonals bisect each other)

Give the most descriptive name

Answer Quadrilateral (Diagonals do not have to be same length or bisect each other. Could look like diagram below: )

Give the most descriptive name

Answer Quadrilateral (Could be either trap or parallelogram, so not enough info to classify)

Give the most descriptive name

Answer Kite (One diagonal is perp. bis. of the other, so the Equidistance Theorem applies)

Give the most descriptive name

Answer Rhombus (Bisecting diagonals means it must at least be a parallelogram, but 4 congruent sides makes it a rhombus.)

Give the most descriptive name

Answer Quadrilateral – Could be isos. trapezoid, but could also be parallelogram since it is not stated that sides of length 8 AREN’T parallel… categories don’t overlap, so it is only known that the shape has 4 sides