Report

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 The diagonals of a rectangle bisect its angles. FALSE (draw an EXTREME rectangle!) True/False A kite with all consecutive angles congruent must be a square. TRUE True/False Diagonals of trapezoids are congruent. FALSE – not always! True/False A parallelogram with congruent diagonals must be a rectangle. TRUE True/False Some rhombuses are rectangles. True – some rhombuses also have right angles True/False The diagonals of a rhombus are congruent. False – not always! True/False If the diagonals of a parallelogram are perpendicular, it must be a rhombus. TRUE True/False Diagonals of a parallelogram bisect the angles. FALSE True/False A quadrilateral that has diagonals that bisect and are perpendicular must be a square. FALSE (could be rhombus… right angles not guaranteed) 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? Rectangle Give the most descriptive name: A rectangle with perpendicular diagonals must be what kind of shape? SQUARE Give the most descriptive name A rhombus with consecutive angles congruent must be a: SQUARE Give the most descriptive name: A parallelogram with diagonals that bisect its angles must be a: Rhombus 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.