LESSON 6-1 I can recognize and apply properties of sides and angles of parallelograms I can...
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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 ⊥