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## PowerPoint Slideshow about ' Special Quadrilaterals ' - fagan

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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.

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.

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