Jose Pablo Reyes

Polygon: Any plane figure with 3 o more sides Parts of a polygon: side – one of the segments that is part of the polygon Diagonal – a line that connects two vertices that are not a side Vertex – the point where two segments meet Interior angle – the angle that is formed inside the polygon by two adjacent sides Exterior angle – the angle that is formed outside the polygon by two adjacent sides

Convex polygon – is a polygon in which all vertices point out Concave polygon – is a polygon in which at least one angle is pointing into the center of the figure Equiangular – polygon in which all angles are congruent Equilateral – polygon in which all sides are congruent

Interior angles theorem of quadrilaterals:

Theorem : If a quadrilateral is a parallelogram its diagonals bisect each other converse: if the diagonals of a quadrilateral bisect each other then it is a parallelogram Theorem 6-3-2: If both pairs of opposite sides of a quadrilateral are congruent, then it is a parallelogram converse: if in a quadrilateral both pairs of opposite sides are congruent then it is a parallelogram

Theorem 6-6-2: If a quadrilateral is a kite, then its diagonals are perpendicular converse: if in a quadrilateral the diagonals are perpendicular, then it is a kite Theorem 6-5-2: If the diagonals of a parallelogram are congruent, then it is a rectangle converse: if a rectangle has congruent diagonals, then it is a parallelogram

A quadrilateral is a parallelogram if; - opposite sides are parallel - opposite angles are congruent - opposite sides are congruent - adjacent angles are supplementary - diagonals bisect each other Theorem 6.10:

Squares : 4 sided regular polygon, that has all sides and angles congruent int. angles = 90 2 pairs of parallel lines Rhombuses: quadrilateral with 4 congruent sides its diagonals are perpendicular Rectangles: 4 sided polygon with congruent angles int. angles = 90 diagonals are congruent Two pairs of parallel lines

Theorem 6-4-3: If a quadrilateral is a rhombus, then it is a parallelogram Theorem 6-4-4: If a parallelogram is a rhombus, then its diagonals are perpendicular Theorem 6-4-5: If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles

Theorem 6-4-1: If a quadrilateral is a rectangle, then it is a parallelogram Theorem 6-4-2: If a parallelogram is a rectangle, then its diagonals are congruent

Trapezoid: A quadrilateral with one pair of parallel lines, each parallel side is called a base, and the parts that are not parallel are called legs. Isosceles trapezoid: when the legs are congruent Theorem 6-6-3: if a quadrilateral is an isosceles trapezoid, then each pair of base angles are congruent Theorem 6-6-4: if a trapezoid has one pair of congruent base angles, then the trapezoid is isosceles Theorem 6-6-5: a trapezoid is isosceles if and only if its diagonals are congruent

Theorem 6-6-6: The midsegment of a trapezoid is parallel to each base, and its length is one half the sum of the lengths of the bases

Kite: A quadrilateral with two pairs of congruent consecutive sides Theorem 6-6-1: if a quadrilateral is a kite, then its diagonals are perpendicular Theorem 6-6-2: if a quadrilateral is a kite, then a pair of opposite angles are congruent