Polygons and quadrilaterals

This set has all the theorms you need to know for proofs involving polygons and quadrilaterals

Poly angle-sum theorem

The sum of the measures of the interior angles of a n-gon is: (n-2)•180

collaroy to angle-sum theorem

The sum of the measures of the interior angles of a n-gon is (n-2)•180/n

Polygon Exterior Angle Sum Theorem

The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360.

Theorem 6-3-1 (conditions for parallelograms)

If a quadrilateral is a parallelogram, then its opposite sides are congruent.

consecutive angles

angles of a polygon that share a side

theorem 6-4

if a quadralateral is a parrlleagram then its consecutive angles are suplementary

therom 6-5

if a quadrilateral is a parallelogram then its opposite angles are congruent

theorem 6-6

If a quadrilateral is a parallelogram, then its diagonals bisect each other.

theorem 6-7

If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

theorem 6-8

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram

theorem 6-9

If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram.

theorem 6-11

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

theorem 6-12

If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.

theorem 6-13

If a parallelogram is a rhombus, then its diagonals are perpendicular.

theorem 6-14

If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles

theorem 6-15

If a parallelogram is a rectangle, then its diagonals are congruent.

theorem 6-16

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

theorem 6-17

If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus.

theorem 6-18

If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

theorem 6-19

If a quadrilateral is an isosceles trapezoid, then each pair of base angles is congruent.

theorem 6-20

If a quadrilateral is an isosceles trapezoid, then its diagonals are congruent.

theorem 6-21

If a quadrilateral is a trapezoid, then (1) the mid segment is parallel to the bases, and (2) the length of the mid segment is half the sum of the lengths of the bases.

theorem 6-22

If a quadrilateral is a kite, then its diagonals are perpendicular.