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# Special Quadrilaterals - PowerPoint PPT Presentation

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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Presentation Transcript

Honors Geometry

True/False

Every square is a rhombus.

True/False

If the diagonals of a quadrilateral are perpendicular, then it is a rhombus.

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.

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.