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Quadrilaterals

Quadrilaterals. Bryce Hall 4 Wennersten. Parallelograms. Definition: a quadrilateral having both pairs of opposite sides parallel to each other . Properties. The opposite sides are parallel The opposite sides are also congruent The opposite angles are congruent

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Quadrilaterals

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  1. Quadrilaterals Bryce Hall 4 Wennersten

  2. Parallelograms Definition: a quadrilateral having both pairs of opposite sides parallel to each other.

  3. Properties • The opposite sides are parallel • The opposite sides are also congruent • The opposite angles are congruent • The diagonals bisect each other Bisects

  4. Formulas for Parallelograms • Perimeter = 2a + 2b • Area = b x h • The area is b x h because a parallelogram is basically just two right triangles and a rectangle, so the area = length x width and length x width = b x h :3

  5. Properties we don’t Know • The adjacents sides are parallel, so their measure is 180° x + y = 180°

  6. Rhombus • Definition: an equilateral parallelogram, including the square as a special case.

  7. Properties of Rhombuses • Have 4 equal/congruent/same sides • Their diagonals are perpendicular • Diagonals make right triangles • The diagonals bisect their angles

  8. Formulas • Perimeter = all four sides added together • x + x + x +x (x4) = perimeter • Area = length of 2 diagonals times ½ • Area = ½ab

  9. Properties of the Angles of a Rhombus(Stuff we don’t know yet) • Adjacent sides of Rhombus are supplementary (Add up to 180°)

  10. Rectangles Definition: a parallelogram having four right angles. gay rectangle

  11. Properties of Rectangles • Four right angles (all 90°) • Diagonals are congruent This picture is a rectangle!!!

  12. Formulas of Rectangles • Perimeter is the two lengths and the two heights added together • l + l + w + w = perimeter • Area is the length times the width • l x w = height

  13. Special Quadrilaterals!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

  14. Trapezoids • Definition: a quadrilateral plane figure having two parallel and two nonparallel sides

  15. Properties of Trapezoids • Only have one set of parallel sides • The midsegment is the average of the base lengths • The midsegment is parallel to the bases • The angles on either side of the base are parallel • The diagonals are congruent • The adjacent angles are parallel (Add up to 180°) b = base, a = leg

  16. Formulas of Trapezoids • Perimeter is the length of every side • leg1 + leg2 + base1 + base2 = perimeter • Area is the ½ of the height times both of the bases added together • Area = ½ h (b + b)

  17. Why we use the formula ½ h (b + b) for area of a Trapezoid • The formula is based on two identical trapezoids side by side, so they’re a parallelogram!!!! • We have to use the formula for parallelograms ( base x height) • Since the are of this figurative parallelogram is two of the trapezoids, we find ½ of it!!!!!!!!

  18. Kites • There’s no definition, but it looks like a kite! Gay kite!

  19. Properties of a Kite • Two pairs of congruent sides • Two of the sides aren’t congruent • The diagonals are perpendicular • One pair of the opposite angles are congruent • The intersection of the diagonals make right triangles (Because they’re perpendicular) • The long diagonal bisects the short one

  20. Formulas for Kites • The perimeter is all of the sides added • a + a + b + b = perimeter • Add the two diagonals and divide by 2 or multiply by ½ • area = ½ ab

  21. Isosceles trapezoids • There’s no definition, but an isosceles trapezoid has one pair of equal sides!!!!!!! (Isosceles trapezoids have the same formulas as normal trapezoids!)

  22. Properties of Isosceles Trapezoids • Pairs of the base angles are congruent • Diagonals are congruent • The angles on either side of the bases are the same size

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