arallelogram: quadrilateral with two pairs of sides. sides are parallel Opposite sides are Opposite angles are onsecutive angles are iagonals each oth
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1 olygon: shape formed by three or more segments (never curved) called. Each side is attached to one other side at each endpoint. The sides only intersect at their. The endpoints of the sides (the corners of the polygon) are called (each one is a vertex). Two vertices that are the endpoints of the same side are called vertices. of a polygon is a segment that joins two non-consecutive vertices (sides are not diagonals). Hexagon EF lassifying olygons Number of ides ore than 12 Type of olygon side F E diagonal vertex consecutive vertices Examples: ecide whether each figure is a polygon. If it is, say what type it is. If it isn t, explain why not. Quadrilateral Interior ngles Theorem: The measures of the interior angles of a quadrilateral add up to. m + m + m + m = 360 Examples: Find the missing angle measures in each quadrilateral. Q Examples: Find the value of the variable in each quadrilateral. 12 (7x + 14) 4 62 (2y) 8 13
2 arallelogram: quadrilateral with two pairs of sides. sides are parallel Opposite sides are Opposite angles are onsecutive angles are iagonals each other Examples: Find and in. Find the missing angle measures in Q. Q is a parallelogram. Find the requested measures. Find N and N. Find N and N if = 20. N N 7 Find the value of the variables in each parallelogram. 1 x x 1 (4x + ) 14 2y + 3 In the diagram below, WXYZ is a parallelogram. Find the requested measures. W X m XWZ = YZ = m WXY = Z = m WZ = WY = m WX = WZ =.3 28 Z 7 63 Y 4y + 4
3 To rove that a Quadrilateral is a arallelogram: how that both pairs of opposite sides are. how that both pairs of opposite sides are. how that both pairs of opposite angles are. how that one angle is to both of its consecutive angles. x x + = 180 how that the bisect each other. how that one pair of sides is both and. Examples: ecide whether each quadrilateral is a parallelogram. Explain your reasoning. Hint: On each problem, list everything that the diagram tells you. Then think about whether you can use that information to say anything else about the diagram. Finally, decide whether you have enough information to use one of the theorems above
4 ectangle: parallelogram with four angles. ll properties of parallelograms apply (ectangles are parallelograms) Four angles diagonals ectangle orollary: If a quadrilateral has four right angles, then it is a. This means you don t have to know that it is a parallelogram to show it is a rectangle. Examples: Each of the quadrilaterals below is a rectangle. Find the requested values. If O = 10, find N,, and N. Find the value of x. Find the value of y, EG and G. N Q E F O T x H G EG = 3y + FH = 6y hombus: parallelogram with four. ll properties of parallelograms apply (hombi are parallelograms) ll four sides are iagonals are Each diagonal bisects a pair of angles hombus orollary: If a quadrilateral has four sides, then it is a. This means you don t have to know that it is a parallelogram to show it is a rhombus. Examples: Each of the quadrilaterals below is a rhombus. Find the requested values. Find,, and. Find the value of x. Find the values of y and z. 3x x z quare: parallelogram with four sides and four angles. ll properties of apply (ll squares are ) ll properties of apply (ll squares are ) ll properties of apply (ll squares are ) quare orollary: If a quadrilateral has four sides and four right angles, then it is a. This means you don t have to know that it is a parallelogram to show it is a square.
5 Trapezoid: quadrilateral with exactly one pair of sides. of a trapezoid: The parallel sides of a trapezoid. air of ase ngles eg ase angles: Two angles that share a. air of ase ngles trapezoid has two pairs of base angles. of a trapezoid: The non-parallel sides of a trapezoid. ase The angles on either side of each leg are (ame-side interior angles). ase eg idsegment of a trapezoid: The segment that joins the of the legs. midsegment roperties of the midsegment of a trapezoid: + E F the legs (definition) EF = 2 to the two bases ength is the average of the lengths of the bases (add the lengths of the bases and divide by two). Isosceles Trapezoid: trapezoid with. iagonals are. ase angles are. Examples: Find the missing angle measures. Find the length of midsegment N. Find. U 14 T 8 N W V T 13 U Q is an isosceles trapezoid. is an isosceles trapezoid. is an isosceles trapezoid. Find the missing angle measures. Find the value of x. Find if = 10. Q 4x ite: quadrilateral with two pairs of consecutive sides and no opposite sides. No parallel sides iagonals are perpendicular.
6 irections: ut an x in the box if the statement is always true for each type of quadrilateral. oth pairs of opposite sides are parallel iagonals are oth pairs of opposite angles are iagonals bisect each other ll pairs of consecutive angles are supplementary iagonals are perpendicular Exactly one pair of parallel sides oth pairs of opposite sides are ll four sides are iagonals are angle bisectors Has four right angles arallelogra m ectangle hombus quare Trapezoid Isosceles Trapezoid
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November 10, 2004 : Fax:
Honors Geometry Issue Super Mathter November 0, 004 : 30-0-6030 Fax: 30--864 For class info, visit www.mathenglish.com irect your questions and comments to rli@smart4micro.com Name: Peter Lin Peter Lin