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LESSON 6-1

I can recognize and apply properties of sides and angles of parallelograms

I can recognize and apply properties of the diagonals of a parallelogram

quadrilateral

parallel

parallel

congruentcongruentsupplementary

bisect each other

6 cm

8 cm115°65°

65°

2a = 34

17

8b = 112

14

68°

55°60°

5x + 55 + 60 = 180 2y + 55 + 60 = 180

13

32.5

6x + 12x = 180

x = 10

60° 120°

3y = 120

y = 40

10

40

24.5 24.5

51° 129°

51° 129°

3x + 14 = 7x

x = 3.5

2z – 3 + 5z – 6 = 180

x = 27

6x = 24

4

4y = 18

4.5

12 12

9 18

24 9

3w = w + 8

w = 4

4z – 9 = 2z

z = 4.5

EF Opp sides are parallel

GF Opp sides are congruent

EH Diagonals bisect each other

∠FGD Opp angles are congruent

∠DEF

Consec angles are suppl.∠DGF

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8-2 worksheet

ASSIGNMENT

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LESSON 6-2

I can recognize the conditions that ensure a quadrilateral is a parallelogram

I can prove that a set of points forms a parallelogram in the coordinate plane

slopem = 3/5

m = 3/5

AB DC∥ AD BC∥and

slope AB =

slope DC =

slope AD =

slope BC =

– 1

5

– 1

5

3

1

3

1

AB DC≅ AD BC≅and

AB =

DC =

AD =

BC =

√26

√26√10√10

diagonals bisect each other

mp of AC =

mp of BD =

(0, 1)

(0, 1)

Q

R

S

T

Diagonals DON’T bisect each other

mp of TR =

mp of SQ =

(-1.5, 2)

(-2, 0)

parallelslope formula

AB CD∥ AC BD∥congruent

distance formula

AB CD≅ AC BD≅

bisectmidpoint formula

mp of AD = mp of CB

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6-2 worksheet

ASSIGNMENT

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LESSON 6-3

I can recognize and apply properties of rectangles

I can determine whether parallelograms are rectangles

quadrilateral

4 right angles

parallel

congruent90°

supplementary

bisect each other

congruent

Are congruent

R S

UT

6x + 3 = 7x – 2

5 = x

R S

TU

6y + 2 = 4y + 6

y = 2

6x + 3 = 7x – 2

x = 5

66

33

8x + 3 + 16x – 9 = 90

24x – 6 = 90

x = 4

m∠STR = 35°

10x + 7 = 6x + 23

x = 4

?47°

m∠ACD = 90 – 47 = 43°

3x + 6 + 5x – 4 = 90

x = 11

?

39°

m∠ADB = 39°

8 cm 6 cm

10 cm

6

8

c 62 + 82 = c2

100 = c2

10 = c

5 cm53°

53° 37°

37°37° 37°

106°

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6-3 worksheet

ASSIGNMENT

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LESSON 6-4

I can recognize the conditions that ensure a quadrilateral is a rectangle

I can prove that a set of points forms a rectangle in the coordinate plane

m = 3/5

m = -5/3

slopesopposite reciprocals

3

5 • –

5

3= -1

slope of AB =

slope of BC =

slope of CD =

slope of DA =

3/1-1/3

3/13/1

AB ⊥ BC, BC ⊥ CD,

CD ⊥ DA, and DA ⊥ AB

3/1

-1/3

3/1

-1/3

mp of AC =

mp of BD =

(0.5,0.5)

(0.5, 0.5) parallelogram

Dist AC =

Dist BD =

√50√50 rectangle

Diagonals bisect each other AND are congruent

BG

HL

mp of LG =

mp of BH =

Dist LG =

Dist BH =

(2.5,4.5)

(2.5, 4.5)

√34√26

parallelogram

Not a rectangle

Diagonals are not congruent

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6-4 worksheet

ASSIGNMENT

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LESSON 6-5

I can recognize and apply the properties of rhombi

I can recognize and apply the properties of squares

quadrilateral 4 congruent sides

parallel

congruentcongruent

supplementary

bisect each other

congruent

are perpendicular

90°

58° 58°

32°

60°

90°

30°

60°

60°60°30°

30°30°

60°

120° 30°

30° 60°

26 10 48

2x + 4 = 4x – 4

x = 4

2x + 4

4x – 4

12

Perimeter = 4(12) = 48

3y – 1 = 8

y = 33y – 1 8

12

5

52 + 122 = c2

169 = c2

13 = c

c

Perimeter = 52

quadrilateral

rhombusrectangle

parallelcongruent

congruent

90°supplementary

congruent

bisect each otherare congruent

are perpendicular

parallelogram

rectanglerhombus

square

diagonals bisect AND ≅diagonals bisect AND ⏊

diagonals bisect

diagonals bisect, ≅ AND ⏊

16

45°

16

16

16

16 16

162 + 162 = c2

512 = c2

22.6 = c

22.6 11.3

45°

90° 45°

45° 90°

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6-5 worksheet

ASSIGNMENT

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LESSON 6-6

I can recognize the conditions that ensure a quadrilateral is a rhombus or square

I can prove that a set of points forms a rhombus or square in the coordinate plane

STEPS:1. CHECK IF THE SHAPE IS A PARALLELOGRAM.

Use midpoint formula to see if the diagonals bisect

2. CHECK IF THE SHAPE IS A RECTANGLE.Use distance formula to see if the diagonals are congruent

3. CHECK IF THE SHAPE IS A RHOMBUS.Use slope formula to see if the diagonals are perpendicular

4. IF THE ANSWER IS “YES” TO ALL OF THE ABOVE, THE FIGURE IS ALSO A … SQUARE

mp of AC =

mp of BD =

Dist AC =

Dist BD =

slope AC =

slope BD =

(-0.5, 1.5)

(-0.5, 1.5)

√26√26

1

5

– 5

1

parallelogram

rectangle

rhombus

Q

S

R

mp of QS =

mp of RT =

Dist QS =

Dist RT =

slope QS =

slope RT =

(-2, 2)

(-2, 2)

√100√ 400

6

8

– 16

12

=

3

4

= – 4

3

T

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6-6 worksheet

ASSIGNMENT

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LESSON 6-7

I can recognize and apply the properties of trapezoids

I can solve problems involving the medians of trapezoids

half sumbases

MN = HJ + LK

2

Median is the average of the bases

parallel

supplementary

congruentsupplementary

congruentare congruent

180° 180°

32

60MN = 32 + 60

2= 46

?

6876

76 = 68 + x

2

= 84

?

46

3x + 5

2= 30

+ 9x – 5

= 6012x

20

x = 5

40

180 – 85 = 95°

180 – 35 = 145°

58

70°

110°

110°

X Y

2422

∠JKE ∠YXE

V W66.5

83°

61

D

B

C

A

Need to show one pair of sides are parallel

slope AD =

slope BC =

2

4

3

6

= 1

2

= 1

2

AD BC∥

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6-7 worksheet

ASSIGNMENT

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LESSON 6-8

I can recognize and apply the properties of kites

I can use the quadrilateral hierarchy

quadrilateralconsecutive

congruentperpendicular

end

end

congruent

bisects

12

12 12

92 + 122 = c2

225 = c2

15 = c

15 15

122 + 162 = c2

400 = c2

20 = c

20 20

90° 37°

2x + 7 = 21

x = 7

21

9 9

D

A

CB

Dist AB =

Dist BC = 

 Dist CD =

Dist DA =

 

 

AB BC≅ CD DA≅and

Quadrilateral

KiteTrapezoid

Trapezoid

Isosceles Trapezoid

Parallelogram

Rectangle

Parallelogram

Square

Rhombus

Quadrilateral

TrapezoidKite

Parallelogram Isosceles Trapezoid

Rhombus Rectangle

Square

XTrue

FalseFalse

FalseTrue

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6-8 worksheet

ASSIGNMENT

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LESSON 6-9

I can construct a

• Parallelogram• Rectangle• Rhombus• Square

bisect

bisect are ≅

bisect are ⊥

bisect are ≅ are ⊥