Transcript Quadrilateral Proofs - Camden Central School

Quadrilateral Proofs
Quadrilateral Classification
Quadrilateral
Parallelogram
Rectangle
Trapezoid
Rhombus
Isosceles
Trapezoid
Square
Proving a quadrilateral is a parallelogram
you may do any of the following:
* Prove two pairs of opposite sides parallel
* Prove two pairs of opposite sides congruent
* Prove one pair of opposite sides both parallel and
congruent
* Prove the diagonals bisect each other
Proving a quadrilateral is a rectangle, first
prove the figure is a parallelogram and
then use one of the following approaches:
* Prove two adjacent sides perpendicular
* Prove one angle is a right angle
* Prove the diagonals are congruent
Proving a quadrilateral is a rhombus, first
prove the figure is a parallelogram and
then use one of the following approaches:
* Prove one pair of consecutive sides congruent
* Prove diagonals bisect the angles
* Prove diagonals are perpendicular to each other
Proving a quadrilateral is a square, first
prove the figure is a parallelogram and
then use one of the following approaches:
* Prove one pair of consecutive sides congruent
and at least 1 right angle
* Prove diagonals bisect the angles and one pair of
consecutive sides is congruent
* Prove diagonals are congruent and perpendicular
to each other
* Prove diagonals are congruent and one pair of
consecutive sides congruent
Proving a quadrilateral is a trapezoid:
* Prove only one pair of opposite sides is parallel
Proving a quadrilateral is an isosceles trapezoid,
first prove the figure is a trapezoid and then use
one of the following approaches:
* Prove the non-parallel sides are congruent
* Prove the diagonals are congruent
* Prove one pair of base angles are congruent
YES
YES
YES
YES
NO
Two non-parallel
sides are
congruent
YES
YES
YES
YES
Only Two
sides are
parallel
Two noncongruent sides
are parallel
YES
YES
YES
YES
NO
NO
YES
YES
YES
YES
NO
NO
YES
YES
YES
YES
NO
NO
NO
YES
NO
YES
NO
NO
NO
NO
NO
NO
NO
NO
YES
NO
YES
NO
NO
All angles
congruent
NO
YES
NO
YES
YES
NO
YES
YES
YES
YES
YES
All angles
congruent
NO
NO
NO
NO
NO
NO
YES
NO
NO
NO
NO
YES