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Parallelograms

Parallelograms. Yanique Bell Olivia Amanda Tiffany. General Information. What is a parallelogram? A parallelogram is a quadrilateral that has two pairs of opposite sides that are parallel and congruent. Important Formulas: Perimeter= 2a+2b or a+a+b+b Ex: a= 3 b=7 P= 2(3)+2(7) P=20

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Parallelograms

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  1. Parallelograms Yanique Bell Olivia Amanda Tiffany

  2. General Information • What is a parallelogram? • A parallelogram is a quadrilateral that has two pairs of opposite sides that are parallel and congruent. • Important Formulas: • Perimeter= 2a+2b or a+a+b+b Ex: a= 3 b=7 P= 2(3)+2(7) P=20 • Area= bh Ex: b=4 in. h=6 in. A=24 in.2 Any of the sides may be the base. The altitude or height is the segment perpendicular to the base and ends on an endpoint of the parallelogram. It can be inside or outside the parallelogram.

  3. Properties of Sides • The opposite sides of a parallelogram are congruent. How do we know this is true? Properties of Sides

  4. Properties of Angles • Opposite angles of a parallelogram are congruent. • Consecutive angles are supplementary. Consecutive angles- angles that are adjacent or next to each other. How do we know this is true? Properties of Angles

  5. Properties of Diagonals • If a quadrilateral is a parallelogram then… • The diagonals bisect each other • The diagonals form two sets of congruent triangles

  6. How do we know this is true? B A Given: ABCD is a parallelogram Prove: AO=OC BO=OD O D C Statements Reasons ABCD is a parallelogram 1) Given 2) AB||DC 2) Definition of a parallelogram (1) 3) <BAC = <ACD 3) Alt. Int. Angles Theorem (2) [A] 4) <BDC = <ABD 4) Alt. Int. Angles Theorem (2) [A] 5) AB=DC 5) Definition of a parallelogram (1) [S] 6) ABO= CDO 6) ASA Postulate (3,4,5) 7) AO=OC 7) CPCTC (6) 8) BO=OD 8) CPCTC (6)

  7. How do we know this is true? B A Given: AD = BC, AB=DC Prove:ABCD is a parellelogram 3 2 1 D 4 C Statements Reasons AD=BC, AB=DC 1) Given 2) BD=BD 2) Reflexive Property 3) Triangle ABD=tri. CDB 3)SSS Post. 4) <1= <2 4)CPCTC 5)AD parel. BC & AB par. DC 5)If alt. inter. Angle c= 6. ABCD parel. 6)2 sets paral.)

  8. Geometer’s Sketchpad: Properties of Diagonals All Properties

  9. Lines of Symmetry • By using paper folding, we can see that parallelograms have no lines of symmetry. • A parallelogram that is not a rectangle or rhombus can be symmetrically rotated by 180o

  10. Suggested Websites • www.mathopenref.com/parallelogram.html • http://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/ • http://www.ies.co.jp/math/products/geo1/applets/para/para.html

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