# CHAPTER 6. Polygons, Quadrilaterals, and Special Parallelograms

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1 CHAPTER 6 Polygons, Quadrilaterals, and Special Parallelograms

2 Table of Contents DAY 1: (Ch. 6-1) SWBAT: Find measures of interior and exterior angles of polygons Pgs: 1-7 HW: Pgs: 8-10 DAY 2: (6-2) Pgs: HW: Pgs: SWBAT: Solve Problems involving Parallelograms DAY 3: (6-4) Pgs: HW: Pg: 23 SWBAT: Solve Problems involving Rectangles DAY 4: (6-4) Pgs: HW: Pgs: SWBAT: Solve Problems involving Rhombi and Squares DAY 5: (6-6) Pgs: HW: Pgs: SWBAT: Solve Problems involving Trapezoids DAY 6-7: (Review) SWBAT: Review of Quadrilaterals Pgs: HW: Finish this section for homework

3 Chapter 6 (Section 1) Day 1 Angles in polygons A polygon is a closed plane figure formed by three or more segments that intersect only at their endpoints. Each segment that forms a polygon is a side of the polygon. The common endpoint of two sides is a vertex of the polygon. A segment that connects any two nonconsecutive vertices is a diagonal. You can name a polygon by the number of its sides. The table shows the names of some common polygons. All the sides are congruent in an equilateral polygon. All the angles are congruent in an equiangular polygon. A regular polygon is one that is both equilateral and equiangular. If a polygon is not regular, it is called irregular. A polygon is concave if any part of a diagonal contains points in the exterior of the polygon. If no diagonal contains points in the exterior, then the polygon is convex. A regular polygon is always convex. Warm Up Tell whether the following polygons are concave or convex and regular or irregular

4 Sum of Interior Angles in Polygons Example 1: Calculating the Sum of Interior Angles Find the sum of the interior angles of a decagon. You Try It! Find the sum of the interior angles of a 14-gon. 2

5 Example 2: Calculating the number of sides of a polygon given the sum of the interior angles The sum of the interior angles of a convex regular polygon measure 1980, how many sides does the polygon have? You Try It! The sum of the interior angles of a convex regular polygon measure 3240, how many sides does the polygon have? 3

6 Interior Angles Formula for any Polygon Example 3: Calculating the measure of each of interior Angle of any regular polygon What is the measure of each interior angle of a regular octagon? You Try It! What is the measure of each interior angle of a regular 12-gon? You Try It! How many sides does a regular polygon have if each interior angle measures 160? 4

7 Exterior Angles Refer to the two polygons below. What do you notice about the exterior angles of any polygon? Example 4: Calculating the measure of an exterior angle given the number of sides or Vice Versa Find the measure of each exterior angle of a polygon with 18 sides. You Try It! Find the measure of each exterior angle of a polygon with 36 sides. 5

8 You Try It! The measure of an exterior angle of a convex regular polygon is 45. Find the number of sides of the polygon. Example 5: Solving Algebraic Problems Find the value of x. Find x: 6

9 Challenge In Exercises 1, find each lettered angle measure. Summary = i = Exit Ticket 7

10 Day 1: Homework 8

11 9

12 10

13 Chapter 6 (Section 2) Day 2 Parallelograms Warm Up Any polygon with four sides is a called a Quadrilateral. However, some quadrilaterals have special properties. These special quadrilaterals are given their own names. Given: 11

14 Given: Identify all angles that are congruent. Properties of Parallelograms If a quadrilateral is a parallelogram, then its opposite angles are congruent. If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. + = = = = 180 Example 1: 12

15 Example 2: Given:,. Find the measure of all the other angles. = = = = If a quadrilateral is a parallelogram, then its opposite sides are congruent. Example 3: Solve for x and y. 13

16 If a quadrilateral is a parallelogram, then its diagonals bisect each other. Example 4: Solve for x and y. BE = 6y - 22, DE = 4y - 4, AE = 3x 2, and AC = 8x

17 You Try It! TX = 4y, YX = 30 XW = y + 3, XZ = 3y + 12 Solve for x and y. = = = 15

18 Summary Homework Exit Ticket 16

19 Homework 17

20 18

21 Warm - Up Chapter 6 (Section 4) Day 3 Rectangles Definition: A rectangle is a parallelogram with one right angle. 19

22 Let s explore the Properties of the rectangle! The diagonals of a rectangle are congruent. The angles of a rectangle are all right angles. If m m 2 = m 3 = m 4 = 20

23 Practice Problems a. If AE = 5, and DC = 8, find AC, BD, AD, and AB. AC = BD = AD = AB = b. If BD = 3x 7 and CA = x + 5, find BD, ED, CA, and AE. BD = ED = CA = AE = c. m 1 = m 2 = m 3 = m 1 = m 2 = m 3 = m 4 = d. 21

24 CHALLENGE In a rectangle, the length is twice the width, and the perimeter is 48. Find the area of the rectangle. SUMMARY Exit Ticket 22

25 Homework 6. 23

26 Chapter 6 (Section 4) Day 4 Rhombi and Squares Warm - Up m 1 = m 2 = 40 m 3 = m 4 = m 5 = m 6 = m 7 = m 8 = 24

27 Rhombus Definition: A quadrilateral with 4 congruent sides. Square Definition: A square is a rectangle with 2 congruent consecutive sides. 25

28 Problems Involving the Squares hj 26

29 Problems Involving the Rhombus If DM = 6y + 4 and ML = 5y + 8, find the length of KL. x = m A = m B = m C = m D = gfgf 27

30 Challenge SUMMARY Exit Ticket 28

31 Homework

32 11. The diagonals of a rhombus are 12 and 16 cm. Find the length of a side of the rhombus. 12. The shorter diagonal of a rhombus measures 18cm. The side of the rhombus measures 41 cm. Find the length of the longer diagonal. 30

33 Warm - Up Chapter 6 (Section 6) Day 5 Trapezoids 31

34 Properties of Isosceles Trapezoids If a quadrilateral is an isosceles trapezoid, then each pair of base angles are congruent. + = = 180 If a quadrilateral is an isosceles trapezoid, then the diagonals are congruent 32

35 33

36 34

37 cm 10 cm 35

38 CHALLENGE SUMMARY Exit Ticket 36

39 37

40 38

41 ground. Find RA. 13. If PQ = 15, and SR = 9, find ST and PS. 39

42 Chapter 6 (Review) Day 6 Warm Up Write the missing terms in the unlabeled sections. 40

43 SUMMARY 41

44 Chapter 6 Review Formulas 1. Find the sum of the interior angles of a heptagon? 2. Each interior angle of a regular convex polygon measures 150. How many sides does the polygon have? 3. The sum of the interior angles of a convex regular polygon measures How many sides does the polygon have? 4. How many sides does a polygon have if each exterior angle measures 36? 5. Find the measure of each exterior angle of regular hexagon ABCDEF?

45 43

46 44

47 45

48 46

49 Parallelograms 1. kjkljkjklj 2. fgfgf 3. Jlkjkj 4. 47

50 Rectangles Quadrilateral ABCD is a rectangle. Find each Measure if m 2 =70. 48

51 Rhombus The diagonals of a rhombus are 32cm and 126 cm. Find the perimeter of the rhombus. 49

52 Square KLMN is a square and NO = 6. Find: The perimeter of a square measures 72cm. Find the length of the diagonal. 50

53 Trapezoids Find the length of the midsegment

54 52

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