Final Exam Review Chapter 8 - Quadrilaterals Geometry Ms. Rinaldi.

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Presentation transcript:

Final Exam Review Chapter 8 - Quadrilaterals Geometry Ms. Rinaldi

Polygon Interior Angles Theorem The sum of the measures of the interior angles of a convex n-gon is (n-2)·180°

Polygon Exterior Angles Theorem The sum of the measures of the exterior angles of a convex polygon is 360°.

Parallelograms Definition: A quadrilateral with both pairs of opposite sides parallel Properties: -Opposite sides are congruent -Opposite angles are congruent -Consecutive angles are supplementary -Diagonals bisect each other

Rhombus Definition: A parallelogram with 4 congruent sides. Properties: -All properties of a parallelogram -Diagonals are perpendicular -Diagonals bisect opposite angles

Rectangle Definition: A parallelogram with four right angles. Properties: -All properties of a parallelogram -Diagonals are congruent

Square Definition: A parallelogram with four congruent sides and four right angles. Properties: -All properties of a parallelogram, rhombus, and rectangle

Trapezoid Definition: A quadrilateral with exactly one pair of parallel sides The parallel sides are the bases. The angles on the same base are called base angles. The nonparallel sides are the legs.

Isosceles Trapezoid Definition: A trapezoid with congruent legs. Properties: -Base angles are congruent -Diagonals are congruent

Midsegment of a Trapezoid Definition: The segment that connects the midpoints of its legs The midsegment is parallel to each base and one half the sum of the lengths of the bases.

Kites Definition: A quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent Properties: -Diagonals are perpendicular -Exactly one pair of opposite angles are congruent

Relationships among Quadrilaterals A square has the most properties, because it is a special type of rectangle, rhombus, and parallelogram.

Relationships among Quadrilaterals