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
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