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Quadrilaterals Project

Quadrilaterals Project. By Alan Gulbierz and Curtis Bohl. Parallelogram. A polygon with four sides Both pairs of opposite sides are parallel Both pairs of opposite sides are congruent One pair of opposite angles are parallel and congruent Both pairs of opposite angles are congruent

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Quadrilaterals Project

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  1. Quadrilaterals Project By Alan Gulbierz and Curtis Bohl

  2. Parallelogram • A polygon with four sides • Both pairs of opposite sides are parallel • Both pairs of opposite sides are congruent • One pair of opposite angles are parallel and congruent • Both pairs of opposite angles are congruent • Diagonals bisect each other

  3. Rectangle • Both pairs of opposite sides are parallel • Both pairs of opposite sides are congruent • One pair of opposite sides are parallel and congruent • Diagonals bisect each other • Both pairs of opposite angles are congruent

  4. Rhombus • Both pairs of opposite sides are parallel • Both pairs of opposite sides are congruent • Diagonals bisects each other • Both pairs of opposite angles are congruent • Consecutive angles are supplementary

  5. Square • Both sides of opposite sides are parallel • Both sides of opposite sides are congruent • One side of opposite sides are congruent and parallel • Diagonals bisect each other

  6. Trapezoid • Exactly are pair of opposite sides are parallel • Exactly two pair of consecutive angles are supplementary

  7. Isosceles Trapezoid • An isosceles trapezoid is a trapezoid with congruent lines • A trapezoid is isosceles of and only if the diagonals are congruent • A trapezoid is isosceles if and only if the base angles are congruent • If a trapezoid is isosceles, the opposite angles are supplementary

  8. Polygons Quadrilaterals Parallelogram Kites Trapezoids Rectangles Rhombi Isosceles Trapezoid Squares Hierarchy of Polygons

  9. Matrix of the properties of special quadrilaterals

  10. Test for parallelograms • If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. • If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. • If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. • If one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram.

  11. Sources • [Roberts, D.](2011). [Theorems and postulates for Geometry.] Retrieved[3/30/11], from http://www.regentsprep.org/regents/math/geometry/GPB/theorems.htm • [Fidelia, B.](2011). [Bella Fidelia's Blog.] Retrieved[3/30/11], from 2.bp.blogspot.com/.../s1600/spongebob.jpg • [Lewis, E.](2011).[Trapezoids.] Retrieved[3/30/11], from www.lutherie.net/trapezoid.martin.jpg • [Williams, R.](2011).[Mandatory celebration isosceles trapezoid.] Retrieved[3/30/11], from 4.bp.blogspot.com/.../s400/al_mahaba.jpg • [HT Staff.](2011).[Hidden Track Review.] Retrieved[3/30/11, from www.glidemagazine.com/.../2009/01/rhombus.jpp

  12. THE END

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