Special Quadrilaterals Practice Honors Geometry
Dec 18, 2015
Give the most descriptive name
A quadrilateral with perpendicular diagonals must be a: _______________
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 quadrilateral in which both diagonals bisect the opposite angles must be a _________________.
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.
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!)
Answer
Quadrilateral
(Diagonals do not have to be same length or bisect each other. Could look like diagram below: )
Answer
Rhombus
(Bisecting diagonals means it must at least be a parallelogram, but 4 congruent sides makes it a rhombus.)