Geometry Chapter 8
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Diagonal of a Polygon
A segment that joins two nonconsecutive vertices of a polygon.

Interior Angles of a Triangle
The angles on the inside of a triangle.

Exterior Angles of a Triangle
The angles on the outside of the triangle.

Theorem 8.1: POLYGON INTERIOR ANGLES THEOREM
 The sum of the measures of the interior angles:
 ( n  2 ) * 180 n = number of sides in a triangle

Corollary To Theorem 8.1: INTERIOR ANGLES OF A QUADRILATERAL
The sum of the measures of the interior angles of a quadrilateral is ALWAYS 360

Theorem 8.2: POLYGON EXTERIOR ANGLES THEOREM
The sum of the measures of the exterior angles of a convex polygon is ALWAYS 360

Parallelogram
A quadrilateral with both pairs of opposite sides parallel.

Theorem 8.3:
If a quadrilateral is a parallelogram, then its opposite sides are congruent.

Theorem 8.4:
If a quadrilateral is a parallelogram, then its opposite angles are congruent.

Theorem 8.5:
If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

Theorem 8.6:
If a quadrilateral is a parallelogram, then its diagonals bisect each other.

Theorem 8.7:
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram

Theorem 8.8:
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Theorem 8.9:
If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.

Theorem 8.10:
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

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.

Square Corollary
A quadrilateral is a square if and only if it is a rhombus and a rectangle.

Theorem 8.11:
A parallelogram is a rhombus if only if its diagonals are perpendicular.

Theorem 8.12:
A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.

Theorem 8.13:
A parallelogram is a rectangle if and only if its diagonals are congruant.

Trapezoid
A quadrilateral with exactly one pair of parallel sides.

Bases of a Trapezoid
The parallel sides of a trapezoid.

Base Angles of a Trapezoid
Trapezoid has 2 pairs of base angles; each pair surrouds a base.

Legs of a Trapezoid
The nonparallel sides of a trapezoid.

Isosceles Trapezoid
Trapezoid with congruent legs.

Midsegment of a Trapezoid
Segments that connects the midpoints of the legs of a trapezoid.

Kite
Quadrilateral with 2 pairs of consecutive congruent sides ( opposite sides are not congruant )

Theorem 8.14:
If a trapezoid is isoceles, then each pair of base angles is congruant.

Theorem 8.15:
If a trapezoid has a pair of congruent base angles, then its an isoceles trapezoid.

Theorem 8.16:
A trapezoid is isosceles if and only if its diagonals are congruent.

Theorem 8.17: 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.

Theorem 8.18:
If a quadrilateral is a kite, then its diagonals are perpendicular.

Theorem 8.19:
If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.