Parallelogram If a quadrilateral has both pairs of opposite sides parallel then

Parallelogram if a quadrilateral has both pairs of

This preview shows page 7 - 10 out of 13 pages.

Parallelogram : If a quadrilateral has both pairs of opposite sides parallel then it is a parallelogram Properties: If a quadrilateral is a parallelogram then it has both pairs of opposite sides parallel 6
If a quadrilateral is a parallelogram then it has both pairs of opposite sides congruent If a quadrilateral is a parallelogram then it has both pairs of opposite angles congruent If a quadrilateral is a parallelogram then it has diagonals that bisect each other If a quadrilateral is a parallelogram then it has one pair of opposite sides parallel and congruent Ways to Prove: If a quadrilateral has both pairs of opposite sides parallel (definition) If a quadrilateral has both pairs of opposite sides congruent If a quadrilateral has both pairs of opposite angles congruent If a quadrilateral has diagonals that bisect each other If a quadrilateral has one pair of opposite sides parallel and congruent Rhombus : If a parallelogram has two adjacent sides congruent, then it is a rhombus. Properties: If a quadrilateral is a rhombus, then all sides are congruent. If a quadrilateral is a rhombus, then the diagonals are perpendicular. If a quadrilateral is a rhombus, then the diagonals bisect the angle to which they are drawn. If a quadrilateral is a rhombus, then the diagonals are perp. bisectors of each other Ways to Prove: If a quadrilateral is a parallelogram with 2 adjacent sides congruent, then the quadrilateral is a rhombus. If a quadrilateral has all sides congruent, then the quadrilateral is a rhombus. If a quadrilateral is a parallelogram whose diagonals are perpendicular to each other, then the quadrilateral is a rhombus. If a quadrilateral is a parallelogram with a diagonal that bisects the angle to which it is drawn, then the quadrilateral is a rhombus. If an angle of a quadrilateral is supplementary to both of its consecutive angles, then it is a parallelogram **All properties of a parallelogram Rectangle: If a parallelogram has at least one right angle, then it is a rectangle. Properties: If a quadrilateral is a rectangle, then all angles are right angles. If a quadrilateral is a rectangle, then the diagonals are congruent. Ways to prove: If a quadrilateral is a parallelogram with one right angle, then the quadrilateral is a rectangle. If a quadrilateral has all angles right angles, then the quadrilateral is a rectangle. If a quadrilateral is a parallelogram whose diagonals are congruent, then the quadrilateral is a rectangle. **All properties of a parallelogram 7
Square : If a rectangle has two adjacent sides congruent then it is a rectangle Properties: If a quadrilateral is a square, then all sides are congruent If a quadrilateral is a square, then the diagonals are congruent If a quadrilateral is a square, then the diagonals are perpendicular If a quadrilateral is a square, then the diagonals bisect the angles to which they are drawn

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture