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Special Quadrilaterals . Honors Geometry. True/False. Every square is a rhombus. TRUE – four congruent sides. True/False . If the diagonals of a quadrilateral are perpendicular, then it is a rhombus. False – diagonals don’t have to be congruent or bisect each other. True/False.
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Special Quadrilaterals Honors Geometry
True/False Every square is a rhombus.
True/False If the diagonals of a quadrilateral are perpendicular, then it is a rhombus.
False – diagonals don’t have to be congruent or bisect each other.
True/False The diagonals of a rectangle bisect its angles.
True/False A kite with all consecutive angles congruent must be a square.
True/False Diagonals of trapezoids are congruent.
True/False A parallelogram with congruent diagonals must be a rectangle.
True/False Some rhombuses are rectangles.
True/False The diagonals of a rhombus are congruent.
True/False If the diagonals of a parallelogram are perpendicular, it must be a rhombus.
True/False Diagonals of a parallelogram bisect the angles.
True/False A quadrilateral that has diagonals that bisect and are perpendicular must be a square.
Sometimes/Always/Never A kite with congruent diagonals is a square.
FALSE – could be, but diagonals don’t have to bisect each other.
Give the most descriptive name: A parallelogram with a right angle must be what kind of shape?
Give the most descriptive name: A rectangle with perpendicular diagonals must be what kind of shape?
Give the most descriptive name A rhombus with consecutive angles congruent must be a:
Give the most descriptive name: A parallelogram with diagonals that bisect its angles must be a:
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.
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.
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.
Proving that a Quad is a Square • If a quadrilateral is both a rectangle and a rhombus, then it is a square.
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.