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Advanced Geometry
* are PLANE figures.
* consist entirely of segments (no curves!).
* consecutive sides intersect only at endpoints
* each vertex belongs to exactly two sides.
* nonconsecutive sides do not intersect
* are closed figures.
NOT a polygon!
* are PLANE figures.
3 – D!
* consist entirely of segments -- no curves!
NOT a polygon!
NOT a polygon!
* are closed figures.
NOT a polygon!
* consecutive sides intersect only at endpoints* nonconsecutive sides do not intersect
X
NOT a polygon!
* each vertex belongs to exactly two sides.
P
2
3
1
Definition: In a convex polygon, each interiorangle has a measure less than 180⁰.
Interior angle greater than 180!
NOT convex!
Concave!
For this class, unless stated otherwise, you should assume that all polygons you work with are convex!
Definition: A diagonal of a polygon is any segment that connects two nonconsecutive (nonadjacent) vertices of the polygon.
Quadrilateral: A four-sided POLYGON
QUADRILATERAL
Parallelogram: A QUADRILATERAL with both pairs of opposite sides congruent and parallel
PARALLELOGRAM
Rectangle: A PARALLELOGRAM in which at least one angle is a right angle
RECTANGLE
Rhombus: A PARALLELOGRAM in which at least two consecutive sides are congruent.
RHOMBUS
Kite: A QUADRILATERAL in which two disjoint pairs of sides are congruent.
KITE
Square: A PARALLELOGRAM that is both arectangle and a rhombus.
SQUARE
rectangle rhombus
Trapezoid: A QUADRILATERAL with exactlyone pair of parallel sides.
TRAPEZOID
one pair of parallel sides.
ISOSCELES Trapezoid: A TRAPEZOID in which the nonparallel sides (called legs) are congruent.
ISOSCELES TRAPEZOID
nonparallel sides are congruent
A B
DC
Upper Base Angles: ∡A and ∡B Lower Base Angles: ∡C and ∡D
LegLeg
The parallel sides are the BASES: AB and CD
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