Honors Geometry Special Quadrilaterals

Fill in all missing angle measures for the RECTANGLE:

Fill in all missing angle measures for the PARALLELOGRAM

Fill in the missing angle measures for the RHOMBUS

Proving that a Quad is a Rectangle If a parallelogram _______________, then it is a rectangle. If a parallelogram _________________, then the parallelogram is a rectangle. If a quadrilateral __________________, then it is a rectangle.

Proving that a Quad is a Rectangle If a parallelogram contains at least one right angle, then it is a rectangle. If a parallelogram has congruent diagonals, then the parallelogram is a rectangle. If a quadrilateral has four right angles, then it is a rectangle.

Proving that a Quad is a Kite If a quadrilateral ________________________, then it is a kite.

Proving that a Quad is a Kite If a quadrilateral has two disjoint pairs of consecutive sides congruent, then it is a kite. If a quadrilateral has one diagonal that is a perpendicular bisector of the other, then it is a kite.

Proving that a Quad is a Rhombus If a parallelogram ______________________, then it is a rhombus. If a parallelogram _______________________, then it is a rhombus. If a quadrilateral _________________________, then the quadrilateral is a rhombus.

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 a parallelogram has either diagonal bisecting opposite angles, then it is a rhombus. If a quadrilateral has diagonals that are perpendicular bisectors of each other, then the quadrilateral is a rhombus.

Proving that a Quad is a Square If a quadrilateral ______________________, then it is a square.

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 a trapezoid _________________________, then it is isosceles.

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.

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 each other and are perpendicular must be a square.

FALSE (could be rhombus… diagonals not guaranteed to be congruent)

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

Geometry in 3D!!!

If parallel lines lie in two distinct planes, the planes must be parallel.

FALSE

Three planes can intersect at a point.

TRUE (ex: corner of classroom)

Three planes can intersect at a line.

TRUE

If two lines in space are not parallel, then they must intersect.

FALSE (Skew lines)

If lines are perpendicular to the same plane, they are parallel.

TRUE

If a line is perpendicular to a line in a plane, then it is perpendicular to the plane.

FALSE (Mailbox problem… must be perp. to two lines in plane passing through foot)

If a line is perpendicular to one of two parallel planes, then it is perpendicular to the other.

TRUE

If a line is perpendicular to a plane, then it is perpendicular to all lines in the plane.

FALSE (Not perp. to lines not passing through its foot)

If separate planes contain skew lines, the planes are parallel.

FALSE

Two planes can intersect at a point.

FALSE (planes continue infinitely)

Two planes can intersect at a line.

TRUE (crack at top of classroom)

Two intersecting lines can lie in more than one plane.

FALSE (intersecting lines determine a plane)

Two parallel lines determine a plane.

TRUE

Two skew lines determine a plane.

FALSE (by definition, skew lines lie in different planes)

Three points determine a plane.

FALSE (must be non- collinear)

If three lines are parallel, then they must be coplanar.

FALSE

In a plane, if two lines are perpendicular to the same line, they are parallel.

TRUE

In space, if two lines are perpendicular to the same line, they are parallel.

FALSE