Advanced Geometry 5 4 5 Four Sided Polygons

Advanced Geometry 5. 4 / 5 Four Sided Polygons / roperties of Quadrilaterals Learner Objective: I will solve problems using properties f special quadrilaterals.

Polygon lane Figure onsists only of segments onsecutive sides intersect only at endpoints on-Consecutive sides do not intersect ach vertex belongs to exactly two sides onvex Polygon polygon in which each interior angle has a measure less than 180. oncave Polygon polygon in which at least one interior angle has a measure greater han 180. iagonal of a Polygon ny segment that connects two nonconsecutive (nonadjacent) ertices of the polygon is a Diagonal of the Polygon.

Quadrilateral: A four sided Polygon Special Quadrilaterals Parallelogram: efinition: A Parallelogram is a Quadrilateral in which both pairs of Properties: pposite sides are congruent pposite angles are congruent iagonals bisect each other Any pair of consecutive angles are supplementary pposite sides are parallel.

Rectangle: efinition: A Rectangle is a Parallelogram in which at least one angle is a roperties: ll properties of a Parallelogram apply by definition ll angles are right angles he diagonals are congruent ight angle.

Rhombus: efinition: A Rhombus is a Parallelogram in which at least two consecutive roperties: ll properties of a Parallelogram apply by definition ll sides are congruent iagonals are perpendicular bisectors of each other iagonals bisect the angles iagonals divide the rhombus into four congruent right triangles ides are congruent.

Square: efinition: A Square is a Parallelogram that is both a Rectangle and a roperties: ll properties of a rectangle apply by definition ll properties of a rhombus apply by definition he diagonals form four isosceles right triangles (45⁰-90⁰) hombus.

Kite: efinition: A Kite is a quadrilateral in which two disjoint pairs of consecutive roperties: iagonals are perpendicular ne diagonal is the perpendicular bisector of the other ne diagonal bisects a pair of opposite angles ne pair of opposite angles are congruent ides are congruent.

Trapezoid: efinition: A Trapezoid is a quadrilateral with exactly one pair of parallel trapezoid. ides. The parallel sides are called bases of the

Isosceles Trapezoid: efinition: An Isosceles Trapezoid is a trapezoid in which the nonparallel roperties: egs congruent by definition ases parallel by definition ower base angles congruent pper base angles congruent iagonals are congruent ny lower base angle is supplementary to any upper base angle ides (legs) are congruent.

quadrilateral parallelogram trapezoid isosceles trapezoid rectangle square rhombus kite Some All No _______ trapezoids are parallelograms _______ rectangles are rhombuses _______ squares are rectangles _______ parallelograms are quadrilaterals _______ isosceles trapezoids are parallelograms _______ rhombuses are squares _______ squares are rhombuses _______ rhombuses are kites _______ trapezoids are rectangles _______ rectangles are parallelograms _______ kites are rhombuses

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