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Polygon Interior Angles Theorem

The sum of the measures of the interior angles of a convex n-gon is (n-2)*180 Interior Angles of a Quadrilateral The sum of the measures of the interior angles of a quadrilateral is 360 degrees

Polygon Exterior Angles Theorem

The sum of the measures of the exterior angles of a convex n-gon, one angle at each vertex, is 360 degrees.

Thm 8.3

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

Thm 8.4

If a quad is a parallelogram, then its oppostie angles are congruent.

Thm 8.5

If a quad is a parallelogram, then its consecutive angles are supplementary.

Thm 8.6

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

Thm 8.7

If both pairs of opposite sides of a quad are congruent, then it is a parallelogram.

Thm 8.8

If both pairs of opposite angles of a quad are congruent, then the quadrilateral is a parallelogram.

Thm 8.9

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

Thm 8.10

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

Rhombus Corollary

A quad is a rhoumbus iff it has four congruent sides.

Rectangle Corollary

A quad is a rectangle iff it has four right angles.

Square Corollary

A quad is a square iff it has four congruent sides and four right angles.

Thm 8.11

A parallelogram is a rhombus iff its diagonals are perpendicular.

Thm 8.12

A parallelogram is a rhombus iff each diagonal bisects a pair of opposite angles.

Thm 8.13

A parallelogram is a rectangle iff its diagonals are congruent.

Thm 8.14

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

Thm 8.15

If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.

Thm 8.16

A trapezoid is isosceles iff its diagonals are congruent.

Midsegment Theorem for Trapezoids

The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.

Thm 8.18

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

Thm 8.19

If a quad is a kite, then exactly one pair of opposite angles are congruent.

Diagonal

A segment that joins two nonconsecutive sides.

Parallelogram

A quadrilateral with both pairs of opposite sides parallel.

Rhombus

A parallelogram with four congruent sides.

Rectangle

A parallelogram with four right angles.

Square

A parallelogram with four congruent sides and four right angles.

Trapezoid

A quadrilateral with exactly one pair of parallel sides.

Bases

The parallel sides of a trapezoid.

Base Angles

The pair of angles on each base of a trapezoid.

Legs

Non parallel sides of the trapezoid.

Isosceles Trapezoid

A trapezoid with congruent legs.

Midsegment of a trapezoid

The segment that connects the midpoints of its legs.

Kite

A quad has two pairs of consecutive congruent sides, but opposite sides are not congruent.

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