Geometry. Kites Families of Quadrilaterals Coordinate Proofs Proofs. Click on a topic to

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1 Geometry Angles of Polygons Properties of Parallelograms Proving Quadrilaterals are Parallelograms Constructing Parallelograms Rhombi, Rectangles and Squares Kites Families of Quadrilaterals Coordinate Proofs Proofs Click on a topic to 1

2 Polygon is a closed figure made of line segments connected end to end. Since it is made of line segments, Can you explain why the figure below is not a polygon? Convex polygons convex if no line polygon contains a point in the interior of the polygon. interior 2

3 Concave polygons interior 1 2 3

4 3 Indentify the polygon. Quadrilateral Hexagon Decagon 4 Is the polygon convex or concave? 5 Is the polygon convex or concave? 4

5 all its sides are congruent. 6 Describe the polygon. (Choose all that apply) Pentagon Concave Quadrilateral Hexagon Equiangular Regular 7 Describe the polygon. (Choose all that apply) Pentagon Concave Quadrilateral Hexagon Equiangular Regular 5

6 8 Describe the polygon. (Choose all that apply) Pentagon Concave Quadrilateral Hexagon Equiangular Regular What do you notice about the regions created by the diagonals? click 1(180 6

7 Given: 180(6-2) = 720 7

8 x = 43 o o o o o +146 o +129 o =540 o o o o polygon is: 9 8

9 regular 20-gon? 9

10 (9x-6), is

11 polygon with n sides is 11

12 o to find n. 12

13 o o Properties of 13

14 Click on the links below and complete the two labs before the Parallelogram lesson. Lab - Investigating Parallelograms Lab - Properties of Parallelograms Parallelograms is a quadrilateral whose both pairs of opposite sides are parallel. D In parallelogram DEFG, If a quadrilateral is a parallelogram, then its opposite sides are congruent. D C 14

15 Theorem Q4 If a quadrilateral is a parallelogram, then its opposite angles are congruent. Theorem Q5 = 180 D 5z C 15

16 D C The consecutive angles are 5z 16

17 D D 17

18 D Theorem Q5 If a quadrilateral is a parallelogram, then the diagonals D C 18

19 sometimes

20

21 Theorem Q6 D C 21

22 Theorem Q7 D C 22

23 23

24 Theorem Q8 D C Theorem Q9 D C Theorem Q10 D C 24

25 25

26 parallel supplementary 26

27 parallel supplementary 27

28 Construct a Parallelogram 28

29 Construct a Parallelogram - Step 1 Construct a Parallelogram - Step 2 Construct a Parallelogram - Step 3 parallelogram? 29

30 3 steps t the length of the segment. 3 steps t 3 steps t Step 3 - Connect the endpoints parallelogram? 30

31 31

32 other. and Squares 32

33 Rhombus Rhombus Corollary D C rhombus? 33

34 rhombus? D C Theorem Q12 34

35 EFGH is a rhombus. EF = HG 2x-6 = 10 = x = 8 are supplementary z = m F z = (108 z = 54 35

36 This is a rhombus. Find x. This is a rhombus. Find x. This is a rhombus. Find x. 36

37 HJKL is a rhombus. Find the length of HJ. Rectangle Corollary A, B, C and D are right angles. rectangle? 37

38 Theorem Q13 D C 63 C 38

39 Square Corollary a properties of a 39

40

41 rhombus Diagonals bisect 41

42 Click on the link below and complete the lab. Lab - Quadrilaterals in the Coordinate Plane trapezoid is a quadrilateral with base base The parallel sides are called bases. The nonparallel sides are called legs. 42

43 isosceles trapezoid Theorem Q14 D C Theorem Q15 43

44 Theorem Q16 BD. D C 44

45 The sum of the interior angles of a quadrilateral is 360 9w = 360 m S = 6w+2 = 6( Option B consecutive interior angles. m P + m S = 180 and m Q + m R = 180 (3w) = 180 m S = 6w+2 = 6( 45

46 46

47 No midsegment of a trapezoid Click on the link below and complete the lab. Theorem Q17 EF = (AB+DC) D C 47

48 48

49 Choose all that apply. 49

50 kites congruent sides. Click on the link below and complete the lab. Lab - Properties of Kites Theorem Q18 B A C D 50

51 (Remember M -1) + 48 = 360 = 242 = 121 ± 51

52 READ is a kite. RE is congruent to. READ is a kite. A is congruent to. 52

53 Find the value of x. o (3x o o D C 53

54 Families of Quadrilaterals 54

55 rhombus parallelogram trapezoid isosceles Description perpendicular rectangle, square of parallel sides Isosceles 55

56 A rhombus is a square. sometimes A square is a rhombus. sometimes A rectangle is a rhombus. sometimes 56

57 A trapezoid is isosceles. sometimes sometimes 57

58 Given: PQRS is a quadrilateral Prove: PQRS is a kite SP = (6-3) PQ = (3-6) 58

59 RQ = (-2-3) + (-3) = (-5) + (-3) = = 34 = 5.83 Prove: JKLM is a square K (4,-1) (-3,0) M K (4,-1) We also know that a square is a rectangle and a rhombus. MJ = (3-0) JK = (-1-3) + (4-1) 59

60 (-3,0) M K (4,-1) (-3) MJ JK and MJ JK MJ LK and JK LM (Opposite sides are congruent) JKLM is a square Given: PQRS is a trapezoid 60

61 Given: TE MA, <1 <2 EM click each pair of opposite sides is parallel and congruent 61

62 Given: FGHJ is a parallelogram, F is a right angle Prove: FGHJ is a rectangle statements Given: COLD is a quadrilateral, m O=140, m D =40 Prove: COLD is a trapezoid 62

63 statements Given: FCD Prove: FD CE FED 63