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Transcript
Advanced Geometry * are PLANE figures. * consist entirely of segments (no curves!). * are closed figures. * consecutive sides intersect only at endpoints * nonconsecutive sides do not intersect * each vertex belongs to exactly two sides. * are PLANE figures. 3 – D! NOT a polygon! * consist entirely of segments -- no curves! 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. 3 P 2 1 NOT a polygon! Definition: In a convex polygon, each interior angle has a measure less than 180⁰. Concave! Interior angle greater than 180! NOT convex! 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 a rectangle rhombus rectangle and a rhombus. SQUARE Trapezoid: A QUADRILATERAL with exactly onepair pairofofparallel parallelsides. sides. one TRAPEZOID ISOSCELES Trapezoid: A TRAPEZOID in which arecongruent. congruent the nonparallel sides sides (called legs) are A Leg B Leg ISOSCELES TRAPEZOID C D The parallel sides are the BASES: AB and CD Upper Base Angles: ∡A and ∡B Lower Base Angles: ∡C and ∡D