Presentation on theme: "Advanced Geometry 5.4 / 5 Four Sided Polygons / Properties of Quadrilaterals Learner Objective: I will solve problems using properties of special."— Presentation transcript:
1 Advanced Geometry5.4 / 5 Four Sided Polygons / Properties of QuadrilateralsLearner Objective: I will solve problems using properties of special quadrilaterals.
2 Polygon Plane Figure Consists only of segments Consecutive sides intersect only at endpoints Non-Consecutive sides do not intersect Each vertex belongs to exactly two sides Convex Polygon A polygon in which each interior angle has a measure less than 180. Concave Polygon A polygon in which at least one interior angle has a measure greater than 180. Diagonal of a Polygon Any segment that connects two nonconsecutive (nonadjacent) vertices of the polygon is a Diagonal of the Polygon.
3 Quadrilateral: A four sided Polygon Special QuadrilateralsParallelogram: Definition: A Parallelogram is a Quadrilateral in which both pairs of opposite sides are parallel.Properties: Opposite sides are congruent Opposite angles are congruent Diagonals bisect each otherAny pair of consecutive angles are supplementary
4 Rectangle: Definition: A Rectangle is a Parallelogram in which at least one angle is a right angle. Properties: All properties of a Parallelogram apply by definition All angles are right angles The diagonals are congruent
5 Rhombus: Definition: A Rhombus is a Parallelogram in which at least two consecutive sides are congruent. Properties: All properties of a Parallelogram apply by definition All sides are congruent Diagonals are perpendicular bisectors of each other Diagonals bisect the angles Diagonals divide the rhombus into four congruent right triangles
6 Square: Definition: A Square is a Parallelogram that is both a Rectangle and a Rhombus. Properties: All properties of a rectangle apply by definition All properties of a rhombus apply by definition The diagonals form four isosceles right triangles (45⁰-45⁰-90⁰)
7 Kite: Definition: A Kite is a quadrilateral in which two disjoint pairs of consecutive sides are congruent. Properties: Diagonals are perpendicular One diagonal is the perpendicular bisector of the other One diagonal bisects a pair of opposite angles One pair of opposite angles are congruent
9 Trapezoid: Definition: A Trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called bases of the trapezoid.
10 Isosceles Trapezoid: Definition: An Isosceles Trapezoid is a trapezoid in which the nonparallel sides (legs) are congruent. Properties: Legs congruent by definition Bases parallel by definition Lower base angles congruent Upper base angles congruent Diagonals are congruent Any lower base angle is supplementary to any upper base angle
12 _______ rhombuses are squares _______ squares are rhombuses quadrilateralparallelogramtrapezoidisosceles trapezoidrectanglesquarerhombuskitekitekiteSomeAllNo_______ rhombuses are squares_______ squares are rhombuses_______ rhombuses are kites_______ trapezoids are rectangles_______ rectangles are parallelograms_______ kites are rhombuses_______ trapezoids are parallelograms_______ rectangles are rhombuses_______ squares are rectangles_______ parallelograms are quadrilaterals_______ isosceles trapezoids are parallelograms