Download Ch. 6 * Polygons and Quadrilaterals

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 6-2-4 : 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
Rectangles:
4 sided polygon with
congruent angles
int. angles = 90
diagonals are congruent
Two pairs of parallel
lines
Rhombuses:
quadrilateral with 4
congruent sides
its diagonals are
perpendicular
 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