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Geometry Chapter 6

Geometry Chapter 6. By: Cate Hogan, Austin Underwood, Paige Mager. Classifying Quadrilaterals. Parallelogram: A quadrilateral with both pairs of opposite sides being parallel Rhombus: A parallelogram with four congruent sides Rectangle: parallelogram with four right angles

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Geometry Chapter 6

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  1. Geometry Chapter 6 By: Cate Hogan, Austin Underwood, Paige Mager

  2. Classifying Quadrilaterals • Parallelogram: A quadrilateral with both pairs of opposite sides being parallel • Rhombus: A parallelogram with four congruent sides • Rectangle: parallelogram with four right angles • Square: parallelogram with four congruent sides and four right angles • Kite: a quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent • Trapezoid: a quadrilateral with exactly one pair of opposite sides

  3. Properties of Parallelograms • Opposite sides of a parallelogram are congruent • Opposite sides are congruent • Opposite angles are congruent • Consecutive angles are supplementary • Diagonals bisect each other • Diagonals form two congruent triangles

  4. Proving That a Quadrilateral is a Parallelogram • If both pairs of opposite sides of a quadrilateral are congruent, it is a parallelogram • If both pairs of opposite angles of a quadrilateral are congruent, it is a parallelogram • If the diagonals of a quadrilateral bisect each other, it is a parallelogram • If one pair of opposite sides of a quadrilateral is both congruent and parallel, then it is a parallelogram

  5. Special Parallelograms • Rhombus: • If one diagonal bisects two angles of a parallelogram, then the parallelogram is a rhombus • If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus • Rectangle: • If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle • Square: • Combine properties previously mentioned in the slide

  6. Trapezoids and Kites • Trapezoid: • Base sides are parallel • The two pairs of angles between the bases are supplementary • Isosceles trapezoid: • Look at properties of a trapezoid • Base angles are congruent • Diagonals are congruent • Kite: • Diagonals are perpendicular • Side angles are congruent • Vertical diagonals form two congruent triangles • Diagonals bisect top and bottom angles

  7. Placing figures in the Coordinate Plane • Consecutive points should be connected segments of the shape

  8. Proofs Using Coordinate Geometry • The midsegment of a trapezoid is parallel to the bases • The length of a midsegment of a trapezoid is (b1+b2) 2

  9. Citations • Prentice Hall Mathematics Geometry Textbook • http://www.google.com/imgres?um=1&safe=active&hl=en&noj=1&biw=1024&bih=585&tbm=isch&tbnid=tVKakCfduEexWM%3A&imgrefurl=http%3A%2F%2Fwww.sparknotes.com%2Ftestprep%2Fbooks%2Fnewsat%2Fchapter20section5.rhtml&docid=XBt3YIVvH7ywqM&imgurl=http%3A%2F%2Fimg.sparknotes.com%2Fcontent%2Ftestprep%2Fbookimgs%2Fnewsat%2F0008%2Ftrapezoid.gif&w=150&h=83&ei=-jXZUsHgIcvOkQer7YGYCw&zoom=1&iact=rc&dur=47&page=1&start=0&ndsp=14&ved=0CF4QrQMwAg • http://www.google.com/imgres?um=1&safe=active&sa=X&hl=en&noj=1&biw=1024&bih=585&tbm=isch&tbnid=FYqSO0UhFpTVBM%3A&imgrefurl=http%3A%2F%2Fshare.ehs.uen.org%2Ftaxonomy%2Fterm%2F237%3Fpage%3D6&docid=s4Hy89s-aY3ywM&imgurl=https%3A%2F%2Fshare.ehs.uen.org%2Fsites%2Fdefault%2Ffiles%2Fimages%2Funit4l2congruent.png&w=191&h=139&ei=bDXZUpW_JpOekAff24CgBQ&zoom=1&iact=rc&dur=4063&page=1&start=0&ndsp=15&ved=0CGcQrQMwBQ • http://www.google.com/imgres?um=1&safe=active&hl=en&biw=1024&bih=585&tbm=isch&tbnid=_iQEMm14LPy6kM%3A&imgrefurl=https%3A%2F%2Fshare.ehs.uen.org%2Fnode%2F14948&docid=OIDrJxasIiXmLM&imgurl=https%3A%2F%2Fshare.ehs.uen.org%2Fsites%2Fdefault%2Ffiles%2Fimages%2Fsquare_0.png&w=147&h=150&ei=0zTZUsiZDs_NkQee8YHADg&zoom=1&iact=rc&dur=3735&page=1&start=0&ndsp=14&ved=0CFYQrQMwAA • http://www.google.com/imgres?um=1&safe=active&hl=en&biw=1024&bih=585&tbm=isch&tbnid=H18yE9rqJTrTnM%3A&imgrefurl=http%3A%2F%2Fen.wikipedia.org%2Fwiki%2FRectangle&docid=BbQmzrq9QCfY4M&imgurl=http%3A%2F%2Fupload.wikimedia.org%2Fwikipedia%2Fcommons%2Fthumb%2F3%2F38%2FRect_Geometry.png%2F220px-Rect_Geometry.png&w=220&h=143&ei=KDTZUri8IYX6kQeUlIGYDQ&zoom=1&iact=rc&dur=3797&page=2&start=10&ndsp=13&ved=0CHoQrQMwDA • http://www.google.com/imgres?um=1&safe=active&sa=N&biw=1024&bih=585&hl=en&tbm=isch&tbnid=Iz_KqUvFofUCpM%3A&imgrefurl=http%3A%2F%2Fmrbgeometry.wordpress.com%2Fquadrilaterals%2Fspecial-quadrilaterals%2F&docid=C0IMKv9_xxs-DM&imgurl=https%3A%2F%2Fmrbgeometry.files.wordpress.com%2F2012%2F03%2Frhombus-mar-24-2012-10-33-am.jpg&w=883&h=701&ei=gjPZUrGWGIO0kQf9vYC4BA&zoom=1&iact=rc&dur=1250&page=1&start=0&ndsp=13&ved=0CG0QrQMwBw • http://www.google.com/imgres?um=1&safe=active&hl=en&biw=1024&bih=585&tbm=isch&tbnid=as3uIIWQqkmqNM%3A&imgrefurl=http%3A%2F%2Fwww.wyzant.com%2Fresources%2Flessons%2Fmath%2Fgeometry%2Fquadrilaterals%2Fproperties_of_parallelograms&docid=UoWo3FOBI5iLQM&imgurl=http%3A%2F%2Fwww.wyzant.com%2FImages%2FHelp%2Fparallelogram1.gif&w=317&h=191&ei=UDrZUoDqLMjvkQeXloGICA&zoom=1&iact=rc&dur=203&page=1&start=0&ndsp=11&ved=0CF8QrQMwAw

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