Geometry quadrilaterals 8
Vocab
Diagonal: diameter; joining 2 non-consecutive vertices in a convex polygon
Interior Angle: angle’s inside the polygon
Exterior Angle: angles formed by extending a side of the figure angle; outside polygon
Parallelogram: Quadrilateral /w both pairs of opposite sides parallel
Rhombus: equilateral parallelogram
Rectangle: equiangular parallelogram
Square: both equilateral and equiangular rectangle
Biconditional:
conditional and converse are both true.
Statement true both ways “if and only if”
⇐>
Convex Polygon - all angles point outwards
Regular Polygon - all sides equal
3 sides: triangle
4 sides: quadrilateral
5 sides: pentagon
6 sides: hexagon
7 sides: heptagon
8 sides: octagon
9 sides: nonagon
10 sides: decagon
11 sides: hendecagon
12 sides: dodecagon
12 + sides:
_
-gon
Interior angle:
Interior angle sum: (n-2)180
Exterior angle:
Exterior angle sum:360
What is the relationship between the interior angle and the exterior angle? They are
supplementary
Theorems
Polygon Interior Angles Theorem
Sum of interior angles = (n-2) 180
“n” is the number of sides in the Polygon
Corollary (only a QUADRILATERAL)
Sum of interior angles of a quad is always 360!
Polygon Exterior Angles Theorem
Sum of the measures of exterior angles of a convex polygon is 360!
m<1+m<2+…+m<n=360 degrees
Parallelogram Quadrilateral ONLY!
parallelogram => opp sides are congruent
parallelogram => oppo angles congruent
parallelogram => consecutive/ss int. angles supplementary (angles next to each other NOT oppo)
parallelogram => diagonals bisect each other
equilateral parallelogram => rhombus
equiangular parallelogram => rectangle
equilateral and equiangular parallelogram => square
Rectangle Corollary
A quadrilateral is a rectangle if and only if It has four right angles
Square Corollary
A quadrilateral is square if and only if it is a rhombus and a rectangle
For da d’est
1 proof = 13 pts
4 questions on polygons — classify polygons by # of sides