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Quadrilaterals ANY four-sided closed figure is a quadrilateral. Rules of a Quadrilateral If a shape has four-sides and is closed then it is a quadrilateral Therefore: There will be four sides There will be four angles The sum of the four angles is 360 degrees How do we know this to be true? How can we be sure that the four angles in quadrilaterals add up to 360 degrees? Because all quadrilaterals can be cut into two triangles BY DRAWING DIAGONALS One triangle (180 degrees) plus another triangle (180 degrees) equals a quadrilateral (360 degrees) How do we know this to be true? How can we be sure that the four angles in quadrilaterals add up to 360 degrees? Because all quadrilaterals can be cut into two triangles BY DRAWING DIAGONALS One triangle (180 degrees) plus another triangle (180 degrees) equals a quadrilateral (360 degrees) Special Quadrilaterals Parallelogram A parallelogram is a special kind of quadrilaterals where both pairs of opposite sides are parallel. Rules of a Parallelogram If a quadrilateral is a parallelogram then the following is true: 1) Opposite sides are congruent 2) Opposite angles are congruent Examples of Parallelograms Here are some types of parallelograms that you may already be familiar with: Rhombus: 1) Opposite Sides are Parallel 2) ALL SIDES ARE CONGRUENT 3) Opposite angles are congruent Examples of Parallelograms Here are some types of parallelograms that you may already be familiar with: Rectangle: 1) Opposite Sides are Parallel 2) Opposite Sides are Congruent 3) FOUR RIGHT ANGLES Examples of Parallelograms Here are some types of parallelograms that you may already be familiar with: Square: 1) Opposite Sides are Parallel 2) ALL SIDES ARE CONGRUENT 3) FOUR RIGHT ANGLES Two Pairs of Parallel Sides A Rhombus, a rectangle, and a square, are all parallelograms because they have two pairs of parallel sides. But what do we call a quadrilateral that only has one pair of parallel sides? Trapezoid A trapezoid is a quadrilateral with only one pair of parallel sides. Rules of a Trapezoid If a quadrilateral is a trapezoid then the following are true: 1) There is exactly one pair of parallel sides. Special Trapezoids Isosceles Trapezoid An isosceles trapezoid is a trapezoid that has congruent non-parallel sides. Rules of Isosceles Trapezoids If a Trapezoid is an isosceles trapezoid then the following is true: 1) There is exactly one pair of parallel sides 2) The NON-PARALLEL sides are congruent 3) There will be TWO PAIRS of congruent angles Quadrilateral Family Tree Quadrilateral Trapezoid Parallelogram Isosceles Trapezoid Rhombus Rectangle Square