Geometry Chapter 6 Flashcards

The sum of the interior angles of a convex polygon is calculated using the formula: 180(n-2)
Each interior angle of a regular polygon is given by: 180(n-2)/n
The sum of the exterior angles of a convex polygon is always 360 degrees.
Each exterior angle of a regular polygon measures: 360/n.

Parallelograms have opposite sides that are parallel and congruent, opposite angles congruent, and diagonals that bisect each other.
Consecutive interior angles in a parallelogram are supplementary, and at least one pair of sides must be both congruent and parallel.

Rectangle: A parallelogram with four right angles; also has congruent diagonals.
Rhombus: A parallelogram with four congruent sides; diagonals are perpendicular and bisect opposite angles.
Square: Combines properties of rectangles and rhombuses; has four right angles and four congruent sides.

All special types (rectangle, rhombus, square) inherit properties of a parallelogram:
- Opposite sides are parallel.
- Opposite sides are congruent.
- Opposite angles are congruent.
- Diagonals bisect each other.
Unique properties:
- Diagonals are congruent in rectangles and squares.
- Diagonals are perpendicular in rhombuses and squares.
- Rectangles and squares feature all angles as right angles.
- Rhombuses and squares have all sides congruent.
- Consecutive angles are supplementary in all types.

Trapezoid: A quadrilateral with exactly one pair of parallel sides.
Isosceles Trapezoid: Has congruent legs; the trapezoid theorem states that the base angles are congruent, and the diagonals are also congruent.
Properties of trapezoids include having one pair of parallel sides and that the length of the mid-segment equals the average of the bases.