Geometry Chapter 7

• parallelogram - quadrilateral with opposite sides are parallel
• Parallelogram Opposite Sides Theorem: If a quadrilateral is a parallelogram, then its opposite sides are congruent
• Parallelogram Opposite Angles Theorem: If a quadrilateral is a parallelogram, then it's opposite angles are congruent
• Parallelogram Consecutive Angles Theorem: If a quadrilateral is a parallelogram, then its consecutive angles are supplementary
• Parallelogram Diagonals Theorem: If a quadrilateral is a parallelogram, then its diagonals bisect each other
• Rhombus Diagonals Theorem: A parallelogram is a rhombus if and only if its diagonals are perpendicular
• Rhombus Opposite Angles Theorem: a parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles
• Rectangle Diagonals Theorem: A parallelogram is a rectangle if and only if its diagonals are congruent
• Trapezoid - quadrilateral with exactly one pair of parallel sides (bases)
• Isosceles Trapezoid - A trapezoid with congruent legs
• Isosceles Trapezoid Base Angles Theorem: if a trapezoid is isosceles, then each pair of base angles is congruent
• Isosceles Trapezoid Base Angles Converse: if a trapezoid has one pair of congruent base angles, then it is an isosceles trapezoid
• Isosceles Trapezoid Diagonals Theorem: A trapezoid is isosceles if and only if its diagonals are congruent
• Midsegment of a trapezoid - a segment that connects the midpoints of a trapezoid's legs
• Trapezoid Midsegment Theorem: A midsegment of a trapezoid is parallel to each base, and its length is 1/2 of the sum of the lengths of bases
• Midsegment of a trapezoid - 1/2(base1 + base2)
• Kite - quadrilateral that has two pairs of consecutive congruent sides, but opposite sides aren't congruent
• Kite Diagonals Theorem: If a quadrilateral is a kite, then its diagonals are perpendicular
• Kite Opposite Angles Theorem: If a quadrilateral is a kite, then exactly on pair of opposite angles are congruent
• Types of Polygons

  Regular: all angles and sides are congruent

  Equiangular: All angles are congruent

  Equilateral: All sides are congruent
• n-gon = 180(n-2)
• Polygon Interior Angles Theorem: The sum of the measures of the interior angles of a convex n-gon is 180(n-2)
• Polygon Exterior Angles: The sum of the exterior angles of a convex polygon is 360 degrees
• Identifying if a quadrilateral is a parallelogram:

  Def of quadrilaterals - if a quadrilateral has 2 pairs of parallel sides

  Parallelogram Opposite Sides Converse - if both pairs of opposite sides of a quadrilateral are congruent

  Parallelogram Opposite Angles Converse: If both pairs of opposite angles of a quadrilateral are congruent

  Opposite Sides Parallel and Congruent Theorem: If one pair of opposite sides of a quadrilateral are congruent and parallel

  Parallelogram Diagonals Converse: If the diagonals of a quadrilateral bisect each other