1 / 64

Polygons 6-1 to 6-5

Polygons 6-1 to 6-5. Find and use the sum of the measures of the interior angles of a polygon. Find and use the sum of the measures of the exterior angles of a polygon. A polygon is an enclosed plane figure that is made up of segments. Diagonal.

samuel-charles
Download Presentation

Polygons 6-1 to 6-5

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Polygons6-1 to 6-5 Find and use the sum of the measures of the interior angles of a polygon. Find and use the sum of the measures of the exterior angles of a polygon.

  2. A polygon is an enclosed plane figure that is made up of segments.

  3. Diagonal • The diagonals of a polygon are the segments that connect any two nonconsecutive vertices.

  4. 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 • n sided n-gon

  5. 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 ...

  6. Polygons Quadrilateral Kite Parallelogram Trapezoid Isosceles trapezoid Rhombus Rectangle Square

  7. 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 vertex is 360. • The measure of each exterior angle of a regular n-gon is 360/n.

  8. Example 1 a • Find the sum of the measures of the interior angles of a convex heptagon. • (n – 2)180 = ( 7 -2)180 • = 5*180 • = 900

  9. 1 b) Find the measure of each interior angle of quadrilateral ABCD. 3x x

  10. Find the sum of the measures of the interior angles of a convex octagon. • (n – 2)180 • (8-2)180 • 6*180 • 1080

  11. Find the measures of eachinterior angle of pentagonHJKLM. 142 2x 2x 3x+14 3x+14

  12. The measure of an interior angle of a regular polygon is 135. Find the number of sides in the polygon.

  13. The measure of an interior angle of a regular polygon is 144. Find the number of sides in the polygon.

  14. Find the value of x. • 2x-5 +5x +2x +6x-5 +3x+10 = 360 • 18x = 360 • X = 20 2x-5 3x+10 5x 2x 6x-5

  15. Find the measure of each exterior angle of a regular nonagon. • 360 = 360 = 40° • n 9

  16. Parallelogram6-2 • A parallelogram is a four-sided figure with both pairs of opposite sides parallel.

  17. Quadrilaterals • Quadrilaterals are four-sided polygons. • <A + <B + <C + <D = 360° A B D C

  18. 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.

  19. 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

  20. 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

  21. Ch = • GF // • <DCG = • DC = • <DCG is supplementary to __ • ∆HGC = C G H D F

  22. 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.

  23. Quadrilateral WXYZ is a parallelogram with m<W = 47. Find the measure of angles X, Y, and Z.

  24. Assignment • Class work on page 407 • problems 1-5, 15-17 • Homework page 408, problems 18-20, 33-36

  25. 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.

  26. Determine whether the quadrilateral is a parallelogram. Justify your answer. • Yes, one pair of sides • are congruent and parallel 14 in 100 80 14 in

  27. 12 5 85 5 85 12 no yes

  28. Find x and y so that each quadrilateral is a parallelogram. 56 5y-26 7x 4y+4

  29. 4y-9 3x+4 5x-2 2y+5

  30. Polygons Quadrilateral Kite Parallelogram Trapezoid Isosceles trapezoid Rhombus Rectangle Square

  31. Rectangle • A rectangle is a quadrilateral with four right angles.

  32. 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

  33. 1. Explain why a rectangle is a special type of parallelogram. • All rectangles are parallelograms, but not all parallelograms are rectangles.

  34. 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

  35. 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

  36. 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

  37. Ex. 5 Quadrilateral JKLM is a rectangle. If m<KJL = 2x +4 and m<JLK = 7x + 5, find x. J K P L M

  38. 6-4 Rhombus • A rhombus is a quadrilateral with four congruent sides.

  39. Assignments6-4 Rectangles • Class work on page 426, problems 10-19 • Homework – problems 26-31

  40. 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

  41. Rhombus A B D C

  42. 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

  43. Square • A square is a quadrilateral with four right angles and four congruent sides.

  44. 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.

  45. Assignment 6-5 • Page 435 • Class work – problems 7-12 • Homework – 23-33

  46. Polygons Quadrilateral Kite Parallelogram Trapezoid Isosceles trapezoid Rhombus Rectangle Square

  47. 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.

  48. base leg leg base

  49. Trapezoid • AB // DC • M<A + m<D = 180 • M<B + m<C = 180 A B D C

  50. Isosceles Trapezoid Properties • The legs are congruent • Both pairs of base angles are congruent • The diagonals are congruent • Angles along the legs are supplementary.

More Related