Studied by 10 peopleThis 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.
Note
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