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Polygons 6-1 to 6-5. Describe Polygons. Recognize and apply properties of sides and angles of quadrilaterals. A polygon is an enclosed plane figure that is made up of segments. Polygons. 3 sided Triangle 4 sided Quadrilateral 5 sided Pentagon 6 sided Hexagon 7 sided Heptagon

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## Polygons 6-1 to 6-5

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**Polygons6-1 to 6-5**Describe Polygons. Recognize and apply properties of sides and angles of quadrilaterals.**A polygon is an enclosed plane figure that is made up of**segments.**Polygons**• 3 sided Triangle • 4 sided Quadrilateral • 5 sided Pentagon • 6 sided Hexagon • 7 sided Heptagon • 8 sided Octagon • 9 sided Nonagon • 10 sided Decagon • 11 sided hendecagon • 12 sided Dodecagon**FYI**• Names of Polygons • 13 triskaidecagon 14 tetrakaidecagon, tetradecagon 15 pentakaidecagon, pentadecagon 16 hexakaidecagon, hexadecagon 17 heptakaidecagon 18 octakaidecagon 19 enneakaidecagon • 20 icosagon 21 icosikaihenagon, icosihenagon 22 icosikaidigon 23 icosikaitrigon 24 icosikaitetragon 25 icosikaipentagon 26 icosikaihexagon 27 icosikaiheptagon 28 icosikaioctagon 29 icosikaienneagon • 30 triacontagon 31 triacontakaihenagon 32 triacontakaidigon 33 triacontakaitrigon 34 triacontakaitetragon 35 triacontakaipentagon 36 triacontakaihexagon 37 triacontakaiheptagon 38 triacontakaioctagon 39 triacontakaienneagon • 40 tetracontagon 41 tetracontakaihenagon 42 tetracontakaidigon 43 tetracontakaitrigon 44 tetracontakaitetragon 45 tetracontakaipentagon 46 tetracontakaihexagon 47 tetracontakaiheptagon 48 tetracontakaioctagon 49 tetracontakaienneagon • 50 pentacontagon ... 60 hexacontagon ... 70 heptacontagon ... 80 octacontagon ... 90 enneacontagon ...**Polygons**Quadrilateral Kite Parallelogram Trapezoid Isosceles trapezoid Rhombus Rectangle Square**Formulas**• The sum of the interiors angle of a convex polygon is (n-2)180. • The measure of each interior angle of a regular n-gon is (n-2)180/n • The sum of the measures of the exterior angles of a convex polygon, one angle at each vertgex is 360. • The measure of each exterior angle of a regular n-gon is 360/n.**Parallelogram**• A parallelogram is a four-sided figure with both pairs of opposite sides parallel.**Quadrilaterals**• Quadrilaterals are four-sided polygons. • <A + <B + <C + <D = 360° A B D C**Properties of a Parallelogram**• Both pairs of opposite sides are parallel. • Both pairs of opposite sides are congruent. • Both pairs of opposite angles are congruent. • The diagonals bisect each other. • Consecutive angles are supplementary.**Diagonal**• The diagonals of a polygon are the segments that connect any two nonconsecutive vertices.**D**C A B • 1. AB // DC, AD // BC • 2. AB =DC, AD = BC • 3. <A = <C and <B = <D • 4. AM = MC and MD = MB • 5. <A + <B = 180 and <B + <C = 180 • <C + <D = 180 and <D + <A = 180**WXYZ is a parallelogram, m<ZWX = b, and m<WXY = d. Find the**values of a, b, c, and d. 2c W X 15 a 18° 31° Y Z 22**Ch =**• GF // • <DCG = • DC = • <DCG is supplementary to __ • ∆HGC = C G H D F**In parallelogram ABCD, AB = 2x +5, m<BAC = 2y, m<B = 120,**m<CAD = 21, and CD= 21. Find the values of x and y.**Quadrilateral WXYZ is a parallelogram with m<W = 47. Find**the measure of angles X, Y, and Z.**Assignment**• Class work on page 407 • problems 9-20 • Homework page 409, problems 31-36**6-3 Tests for Parallelogram**• A Quadrilateral is a parallelogram if any of the following is true. • Both pairs of opposite sides are parallel. • Both pairs of opposite sides are congruent. • Both pairs of opposite angles are congruent. • Diagonals bisect each other. • A pair of opposite sides is both parallel and congruent.**Polygons**Quadrilateral Kite Parallelogram Trapezoid Isosceles trapezoid Rhombus Rectangle Square**Rectangle**• A rectangle is a quadrilateral with four right angles.**Properties of a Rectangle**• Both pairs of opposite sides are parallel. • Both pairs of opposite sides are congruent. • Both pairs of opposite angles are congruent. • The diagonals bisect each other. • Consecutive angles are supplementary • All angles are congruent • The diagonals are congruent**1. Explain why a rectangle is a special type of**parallelogram. • All rectangles are parallelograms, but not all parallelograms are rectangles.**Ex. 2 A rectangular park has two walking paths as shown. If**PS = 180 meters and PR = 200 meters, find QT. Q P • 1A If TS = 120m, find PR • If m<PRS =64, find m<SQR S R**Ex. 3 Quadrilateral MNOP is a rectangle. Find the value of**x. • MO = 2x – 8; NP = 23 • MO = 4x – 13; PC = x + 7 N M O P**Ex. 4 Use rectangle KLMN and the given information to solve**each problem. • M<1 = 70. Find m<2, M<5, M<6 K L 8 1 7 2 C 9 10 6 3 4 5 N M**Ex. 5 Quadrilateral JKLM is a rectangle. If m<KJL = 2x +4**and m<JLK = 7x + 5, find x. J K P L M**6-4 Rhombus**• A rhombus is a quadrilateral with four congruent sides.**Assignments6-4 Rectangles**• Class work on page 426, problems 10-19 • Homework – problems 26-31**Properties of a Rhombus**• Both pairs of opposite sides are parallel. • Both pairs of opposite sides are congruent. • Both pairs of opposite angles are congruent. • The diagonals bisect each other. • Consecutive angles are supplementary • All sides are congruent • The diagonals are perpendicular • The diagonals bisect the opposite angles**Rhombus**A B D C**Use rhombus BCDE and the given information to find each**missing value. C • If m<1 = 2x + 20 and m<2 = 5x – 4, • find the value of x. • If BD = 15, find BF. • If m<3 = y2 + 26, find y. 1 2 3 B D F E**Square**• A square is a quadrilateral with four right angles and four congruent sides.**Properties of a Square**• Both pairs of opposite sides are parallel. • Both pairs of opposite sides are congruent. • Both pairs of opposite angles are congruent. • The diagonals bisect each other. • Consecutive angles are supplementary • All angles are congruent. • The diagonals are congruent. • All sides are congruent • The diagonals are perpendicular. • The diagonals bisect the opposite angles.**Assignment 6-5**• Page 435 • Class work – problems 7-12 • Homework – 23-33**Polygons**Quadrilateral Kite Parallelogram Trapezoid Isosceles trapezoid Rhombus Rectangle Square**6-6Trapezoids and Kites**• Properties of a trapezoid • A trapezoid is a quadrilateral with exactly one pair of parallel sides. • The angles along the legs are supplementary.**base**leg leg base**Trapezoid**• AB // DC • M<A + m<D = 180 • M<B + m<C = 180 A B D C**Isosceles Trapezoid**Properties • The legs are congruent • Both pairs of base angles are congruent • The diagonals are congruent • Angles along the legs are supplementary.**Isosceles TrapezoidAD = BCm<A = m<B, m<D = m<CAC = BDm<A +**m<D = 180m<B + m<C = 180 A B D C**PQRS is an isosceles trapezoid. Find m<P, m<Q, and m<R.**P Q 50° S R**Midsegment of a Trapezoid**• The midsegment of a trapezoid is parallel to the bases, and its measure is one-half the sum of the measures of the bases.**XY = ½(AB + DC)**B A X Y D C**Find the length of the midsegment**• When the bases are • 7 and 11 • 3 and 7 • 12 and 7 • 14 and 16 x**Find x**4 7 x**Find x**15 17 x**Find x**• AB = ½(EZ + IO) 4x - 10 E Z 13 A B I O 3x + 8**Find x**• AB = ½(EZ + IO) 3x-1 E Z 10 A B I O 7x+1**Kite**• Two pairs of consecutive congruent sides. • Diagonals are perpendicular. • Exactly one pair of opposite angles are congruent.

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