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Quadrilaterals

Quadrilaterals. Properties and formulas. Warm-up. What does it mean to be parallel? Lines that never intersect, Line segments that are the same distance apart at every point What does it mean to be congruent? To have the same length What does bisect mean? To cut in half

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Quadrilaterals

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  1. Quadrilaterals Properties and formulas

  2. Warm-up • What does it mean to be parallel? • Lines that never intersect, Line segments that are the same distance apart at every point • What does it mean to be congruent? • To have the same length • What does bisect mean? • To cut in half • What does adjacent mean? • ‘next to’

  3. Today’s Essential Questions Where can I find quadrilaterals in every day life? How are different quadrilaterals related to each other?

  4. What is a quadrilateral? • A closed, 2-dimensional four sided figure where each side is a (straight) line segment. • Types of quadrilaterals • Parallelogram • Trapezoid • Rectangle • Square • Rhombus • Kite

  5. Parallelogram 2 Pairs of parallel sides Both pairs of parallel sides are congruent Opposite angles are congruent If one side is congruent and parallel to another side, then the remain two sides are also congruent and parallel The Diagonals bisect each other

  6. Rhombus A Parallelogram with 4 congruent sides Diagonals are perpendicular, bisect each other, and bisect the angles

  7. Rectangle A parallelogram where all angles are congruent (all 90 degree angles) Diagonals are congruent and bisect each other

  8. Square A parallelogram with 4 congruent sides and 4 congruent angles A rectangle with 4 congruent sides A rhombus with 4 congruent angles (90 degree angles) Diagonals are congruent, perpendicular, bisect each other, and bisect angles

  9. Kite A quadrilateral where each side is congruent to exactly one of the adjacent sides. Diagonals are perpendicular 1 pair of opposite angles are congruent

  10. Trapezoid and Isosceles Trapezoid • A quadrilateral with exactly one pair of parallel sides. (Each called a base) • The non parallel sides are called legs • If the legs are congruent, then the trapezoid is isosceles • An isosceles trapezoid has congruent diagonals and congruent base and top angles

  11. ACTVITY Get out a sheet of paper, and find the following for each shape Share a protractor and a ruler Length of each side (AB,BC,CD, and AD) The measure of each angle (A,B,C, and D) The measure of each diagonal (AC and BD)

  12. A Few More things, Then Review

  13. Warm-Up Find the distance and midpoint of the line segment whose end coordinates are (-2,5) and (3,-7) I saw a figure yesterday with 2 pair of congruent sides, one set of congruent angles, and diagonals that intersected at perpendicular angles. What shape was it?

  14. Trapezoid and Isosceles Trapezoid • A quadrilateral with exactly one pair of parallel sides. (Each called a base) • The non parallel sides are called legs • If the legs are congruent, then the trapezoid is isosceles • An isosceles trapezoid has congruent diagonals and congruent base and top angles

  15. Think about it • Create a mind map using the following words: • Quadrilateral • Square • Parallelogram • Rectangle • Rhombus • Kite • Trapezoid

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