Transcript Review Chapter 6 6.1 - 6.3
Review Chapter 6 6.1 - 6.3
Naming Polygons
# of Sides 3 Type of Polygon triangle 4 5 quadrilateral pentagon # of Sides 8 9 10 12 6 hexagon 7 heptagon n Type of Polygon octagon nonagon decagon dodecago n n-gon
Identifying Convex and Concave
A polygon is convex if no line that contains a side of the polygon contains a point in the interior of the polygon.
A polygon is that is not convex is called nonconvex
Definitions:
A polygon is equilateral if all of its sides are congruent.
A polygon is equiangular if all of its interior angles are congruent.
A polygon is regular if it is both equilateral and equiangular.
Theorem 6.1: Polygon Angle-Sum Theorem
The sum of the measures of the interior angles of an n-gon is (n-2)180.
If you draw a diagonal in a polygon, you create triangles. Using the Triangle Sum Theorem you can conclude that the sum of the measures of the interior angles of a quadrilateral is 2(180)=360 °.
Corollary to Polygon Angle-Sum Theorem The measure of each of the interior angles of a regular polygon is
(
n
2)180
n
(Where n is the number of sides.) Theorem 6.2 Polygon Exterior Angle-Sum Theorem The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360 degrees.
Corollary to Polygon Angle-Sum Theorem The measure of each of the interior angles of a regular polygon is
(
n
2)180
n
(Where n is the number of sides.) Theorem 6.2 Polygon Exterior Angle-Sum Theorem The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360 degrees.
PARALLELOGRAM:
A quadrilateral with both pairs of opposite sides parallel.
Theorem 6.3:
If a quadrilateral is a parallelogram, then its opposite sides are congruent.
Theorem 6.4:
If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.
Theorem 6.5:
If a quadrilateral is a parallelogram, then its opposite angles are congruent.
Theorem 6.6:
If a quadrilateral is a parallelogram, then its diagonals bisect each other.
Theorem 6.7
If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.
If … then…
Theorem 6.8
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Theorem 6.9
If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram.
+ = 180 °
Theorem 6.10
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Theorem 6.11
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Theorem 6.12
If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.
Summary: Proving Quadrilaterals are //grams
Show that both pairs of opposite sides are //.
Show that both pairs of opposite angles are congruent.
Show that both pairs of opposite sides are congruent.
Show that one angle is supplementary to both consecutive angles.
Show that the diagonals bisect each other.
Show that one pair of opposite sides is congruent and parallel.