Today’s Objective

Students will be able classify quadrilaterals and solve for an

interior angles.

Unit 6Lesson 1

Wednesday July 22, 2020 Activator

How do you classify quadrilaterals?

Based on the parallel (II) sides.

Kites have no II sides.Trapezoids have 1 pair of II sides.Parallelograms have 2 pairs of II sides

The sum of all interior angles is 360.

Page #3Lesson 6.1

There are 3 types of quadrilaterals.

Quadrilaterals are differentiated

based on their number of

parallel sides.

Today’s New Vocab (1 of 4)

Page #3Lesson 6.1

Today’s New Vocab (2 of 4)Classify this quadrilateral. Determine the missing angle measure.

56 + 64 + 110 + x = 360230 + x = 360

x = 130-230 -230

This shape is a kite. No parallel sides.The missing angle measure is 130

Page #3Lesson 6.1

Today’s New Vocab (3 of 4)Classify the shape. Determine the value of x.

This shape is a trapezoid. One pair of parallel sides

89+5x–8+3x+4+51 = 3608x+136 = 360

8x = 224

x = 28

-136 -136

÷ 8 ÷ 8

Page #3Lesson 6.1

Today’s New Vocab (4 of 4)Classify the shape. Determine the missing angle.

This shape is a parallelogram. Two pairs of parallel sides.

5x+5x+11x+4+11x+4 = 360 32x + 8 = 360

32x = 352

x = 11 ÷ 32 ÷ 32

- 8 - 811x + 411(11) + 4

121 + 4125

5x 5(11)

55

.

Wednesday July 22, 2020 Work PeriodWhen a quadrilateral is inscribed (inside) in a circle, opposite (across) angles are supplementary (180).

If the measure of <B = 3x and <D=2x,What is the measure of <B and <D?

<B + <D = 1803x + 2x = 180

5x = 180

x = 36÷ 5 ÷ 5

<B = 3x <B = 3(36)<B = 108

<D = 2x <D = 2(36)<D = 72

Page #4Lesson 6.1

3x2x

Wednesday July 22, 2020 Exit ticket

.

Determine the measure of each angle.Classify the quadrilateral.

127 + 10x+7 + 5x+3 + 88 = 36015x + 225 = 360

15x = 135

x = 9÷ 15 ÷ 15

−225 − 225<K = 10x + 7<K = 10(9) + 7<K = 90 + 7<K = 97

<E = 5x + 3<E = 5(9) + 3<E = 45 + 3<E = 48

Today’s Objective

Students will be able to solve problems with parallelograms.

Unit 6Lesson 2

Thursday July 23,2020 Activator For all parallelograms, opposite (across) angles and opposite sides are equal.

100 = 12x - 8

108 = 12x

9 = x

+8 + 8

÷ 12 ÷ 12

2x – 17 = x – 5

x – 17 = – 5

x = 12

-x -x

+17 +17

What is the value of x?

Page #7Lesson 6.2

Today’s New Vocab (1 of 4)For all parallelograms, adjacent angles = 180.Determine m<E.

43x – 1 + 17x + 1 = 180 60x + 0 = 180

60x = 180

x = 3 ÷ 60 ÷ 60

m<E = 43x -1 m<E = 43(3) -1 m<E = 129 -1 m<E = 128

Page #7 Lesson 6.2

Today’s New Vocab (2 of 4)For all parallelograms, what do youknow about opposite sides?Opposite sides are equal.

What is the length of MO? 15

15

What is the value of x? 19

2x + 2 = 40

2x = 38

x = 19

-2 -2

÷2 ÷2 Page #7Lesson 6.2

Today’s New Vocab (3 of 4)For all parallelograms, diagonals bisect (cut in half).Determine the measure of OJ.

40 = x + 18

x + 40 = 2x + 18

22 = x

-x -x

-18 - 18 |OJ| = 2x + 18 |OJ| = 2(22) + 18 |OJ| = 44 + 18 |OJ| = 62

Page #7Lesson 6.2

Today’s New Vocab (4 of 4)

M

Classify the following shape. What is <BMC, <MAD, and <MDA ?

180 = 44 + 46 + <BMC180 = 90 + <BMC

90 = <BMC-90 -90

< MAD = 46 by Alternate Interior Angles< MDA = 44 by Alternate Interior Angles

Parallelogram

“Z angles are equal”

Page #8Lesson 6.2

Thursday July 23, 2020 Work Period

.

2x + 10 + 3x = 1805x + 10 = 180

5x = 170

x = 34

- 10 -10

÷ 5 ÷ 5m<B = 3(34)m<B = 102

m<B = 3x

<A + <B = 180Page #8

Lesson 6.2

Thursday July 23, 2020 Exit Ticket

.

If WXYZ is a parallelogram, what is the measure of <W and <Z?

3x = 84

x = 28 ÷ 3 ÷ 3

<w = 3x<w = 3(28)<w = 84

96 = y + 42

54 = y <z = y + 42 <z = (54) + 42 <z = 96

-42 - 42

Page #8Lesson 6.2

Oppositeangles

are equal.

Today’s Objective

Students will be able to solve problems with Rhombi.

Unit 6Lesson 3

Monday July 27, 2020This is a rhombus. If all of the sides are equal, all of the base angles are equal. What is the measure of Base angles?

100 + x + x = 180 100 + 2x = 180

2x = 80

x = 40 Each angle is 40 degrees.

-100 -100

÷ 2 ÷ 2

Page #11Lesson 6.3

Today’s New Vocab (1 of 3)

2x – 9 = x + 5

x – 9 = + 5

x = 14

−𝑥 − 𝑥

+ 9 + 9

𝐿𝑀 = 2x - 9𝐿𝑀 = 2(14) - 9𝐿𝑀 = 28 - 9

𝐿𝑀 = 19

2x-9

In every Rhombus, all sides are equal.

Page #11Lesson 6.3

What is the length of LM?

Today’s New Vocab (2 of 3)

What is the measure of either angle? 2x + 15 = 5x + 3

+ 15 = 3x + 3

+ 12 = 3x

4 = x

-2x -2x

-3 - 3

÷ 3 ÷ 3

5x + 35(4) + 3

20 + 323

In every Rhombus, the diagonal Bisects (cuts in half) the angle.

Page #11Lesson 6.3

Today (3 of 3)

What is the measure of

<ABC = 120 Why? Diagonals bisect (Half) the angles.<BOA= 90 Why? 180 - 60 - 30 = 90 Triangle Sum<ABO= 60 Why? Diagonals bisect(Half) the angles.

3030

60

90In every Rhombus,

the diagonals are perpendicular 90). 60 60

60

3030

Page #11Lesson 6.3

Monday July 27, 2020 Work Period

.

If AE = 9 and ED = 12, what is the length of one side of rhombus ABCD?

∆𝐴𝐸𝐷 𝑖𝑠 𝑎 𝑟𝑖𝑔ℎ𝑡 𝑇𝑟𝑖𝑎𝑛𝑔𝑙𝑒,𝑦𝑜𝑢 𝑐𝑎𝑛 𝑢𝑠𝑒

𝑃𝑦𝑡ℎ𝑎𝑔𝑜𝑟𝑒𝑎𝑛 𝑇ℎ𝑒𝑜𝑟𝑒𝑚.

𝐴2 + 𝐵2 = 𝐶2

(9)2+(12)2 = 𝑥2

81 + 144 = 𝑥2

225 = 𝑥2

15 = 𝑥

9

12x

Page #12Lesson 6.3

.

Monday July 27, 2020 Exit TicketIn the diagram below of rhombus ABCD, m∠C = 110. What is m∠DBC? 35

Because ∆𝐷𝐵𝐶 𝑖𝑠Isosceles.

X + X + 110 = 1802X + 110 = 180

2X = 70

X = 35

-110 -110

÷2 ÷ 2

x

110x

Page #12Lesson 6.3

Today’s Objective

Students will be able to solve problems with kites and parallelograms.

Unit 6Lesson 5

Monday July 27, 2020 ActivatorClassify the following shape. NL = 24 and KN = 10What is the measure of KL?

𝐴2 + 𝐵2 = 𝐶2

(24)2+ 10 2 = (𝐾𝐿)2

576 +100 = (𝐾𝐿)2

676 = (𝐾𝐿)2 What is the measure of ML?

26 = 𝐾𝐿

KL = ML (26) = ML

Kite

24

x10

Today’s New Vocab (1 of 3)

What is the measure of <FDE?

130

<FDE = 130 Why? Opposite Angles are equal.

130

<A = 50 why? Isosceles Triangles have base angles.

50

What is the measure of <A?

50

Today’s New Vocab (2 of 3)In parallelogram ROCK, what is the m<RSO (x)?

70 x

<R = 70 Why? Opposite angles are equal.

What is the m<RSO?60 + 70 + x = 180

130 + x = 180

x = 50 -130 -130

Today’s New Vocab (3 of 3)In Parallelogram TSRQ,what is the measure of <RTS?

<RTS + <TRS + <S = 180<RTS + 80 + 55 = 180

<RTS + 135 = 180

<RTS = 45-135 -135

< RTS ≅< 𝑇𝑅𝑄 𝑏𝑦 𝐴𝑙𝑡𝑒𝑟𝑛𝑎𝑡𝑒 𝐼𝑛𝑡𝑒𝑟𝑖𝑜𝑟 (𝑍 𝑎𝑛𝑔𝑙𝑒𝑠)

45 + 80 = <R125 = <R

80

55

What is the m<R ?

45

45

.

Monday July 27, 2020 Work PeriodRectangle KLMN has vertices K(0,4), L(5,2), M(2,−4), and N(−3,−2). Determine and state the coordinates of the point of intersection of both diagonals

K L

MN

Midpoint of KM Midpoint of LN

( 0+2

2,4−4

2)

( 1 , 0 )

( 5−3

2,2−2

2)

( 1, 0)

Monday July 27, 2020 Exit Ticket

.

What is the perimeter of this Isosceles Trapezoid?

DG = EF Why? Legs are equal

2x+ 5 = 3x + 2

5 = x + 2

3 = x

-2x -2x

-2 - 2

11

12

1110

10+11+11+12Perimeter = 44

Today’s Objective

Students will be able to review Unit 6 problems about Quadrilaterals.

Unit 6Review

Tuesday July 28, 2020 Activator

#8

.

Today’s New (1 of 4)

90

#6

Today’s New Vocab (2 of 4)

#14

#10

Today’s New Vocab (3 of 4)

.

Because of the Transitive property.

Today’s New Vocab (4 of 4)

#12

Tuesday July 28, 2020 Exit Ticket