Polygon Sum Conjecture

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Polygon Sum Conjecture

• The sum of the measures of the n interior angles
  in a polygon with n sides (an n-gon) is (n-2)180
• Proving the Polygon Sum Conjecture
• A diagonal can be drawn from a single vertex to
  n-3 other vertices, creating a total of n-2
  triangles
• The sum of the measures of the interior angles in
  the polygon equals the sum of the measures of the
  interior angles of the triangles, which is the
  n-2 times 180

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Exterior Angles of a Polygon

• A set of exterior angles of a polygon is created
  by extending each side past each vertex, moving
  in the same direction around the entire polygon
• Each exterior angle and its adjacent interior
  angle form a linear pair
• Exterior Angle Sum Conjecture
• For any polygon, the sum of the measures of a set
  of exterior angles is 360
• Equiangular Polygon Conjecture
• The measure of each interior angle of an
  equiangular polygon with n sides can be found
  by using either of the formulas
• 180(n-2)/n or 180 360/n

3
Kite Properties

• A kite is a quadrilateral with two distinct pairs
  of congruent consecutive sides
• Kite conjectures
• The nonvertex angles of a kite are congruent
• The vertex angles of a kite are bisected by a
  diagonal
• The diagonals of a kite are perpendicular to each
  other
• The diagonal connecting the vertex angles of a
  kite is the perpendicular bisector of the other
  diagonal

U
4
Trapezoid Properties

• A trapezoid is a quadrilateral with exactly one
  pair of parallel sides
• In an isosceles trapezoid the two non-parallel
  sides are congruent
• Trapezoid conjectures
• The consecutive angles between the bases of a
  trapezoid are supplementary
• The base angles of an isosceles trapezoid are
  congruent
• The diagonals of an isosceles trapezoid are
  congruent

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Midsegments

• The midsegment of a triangle is the segment
  connecting the midpoints of two sides of a
  triangle.
• The midsegment of a trapezoid is the segment
  connecting the midpoints of the two nonparallel
  sides of a trapezoid.
• Midsegment Conjectures
• The three midsegments of a triangle divide it
  into four congruent triangles.
• A midsegment of a triangle is parallel to the
  third side and half the length of the third side.
• The midsegment of a trapezoid is parallel to the
  bases and is equal in length to the average of
  the lengths of the bases.

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Parallelograms

• A parallelogram is a quadrilateral with two pairs
  of parallel sides
• A rhombus is an equilateral parallelogram
• A rectangle is an equiangular parallelogram
• A square is an equiangular rhombus or an
  equilateral rectangle or a regular quadrilateral
• Parallelogram Conjectures
• The opposite angles of a parallelogram are
  congruent.
• The consecutive angles of a parallelogram are
  supplementary.
• The opposite sides of a parallelogram are
  congruent.
• The diagonals of a parallelogram bisect each
  other.

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Special Parallelograms

• Rhombus Conjectures
• All conjectures about parallelograms
• If two sets of parallel lines that are the same
  distance apart cross, they create a rhombus.
• The diagonals of a rhombus are perpendicular
  bisectors of each other.
• The diagonals of a rhombus bisect the angles of
  the rhombus.
• Rectangle Conjectures
• All conjectures about parallelograms
• The diagonals of a rectangle are congruent
• Square Conjectures
• All conjectures about parallelograms, rhombuses
  and rectangles
• The diagonals of a square are congruent
  perpendicular bisectors of each other.