chapter 6 – quadrilaterals
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Chapter 6 – Quadrilaterals. In this chapter you will learn about the special properties of quadrilaterals as well as find their perimeters and areas. You will explore the relationships of the sides and diagonals of a parallelogram, kite, trapezoid, rectangle, and rhombus. . 6.1. - PowerPoint PPT PresentationTRANSCRIPT
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In this chapter you will learn about the special properties of quadrilaterals as well as find their perimeters and areas. You will explore the relationships of the sides and diagonals of a parallelogram, kite, trapezoid, rectangle, and rhombus.
Chapter 6 – Quadrilaterals
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6.1
What If Both Sides Are Parallel?Pg. 4
Parallelograms
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6.1 – What If Both Sides are Parallel?_____Parallelograms
In the past, you used your knowledge to find the area of squares and rectangles. But what if the shape didn't have right angles?
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6.1 –PARALLELOGRAMSFind the areas of the figures below. Can you find more than one method for finding the area?
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2 4 2
8 un2
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4
12
4
20 un2
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6.2 –AREA OF A PARALLELOGRAMA parallelogram: a four-sided shape with two pairs of parallel sides. How can you find the area of a parallelogram? Consider this question as you answer the questions below.
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a. Keesha thinks that the rectangle and parallelograms below have the same area. Her teammate Saundra disagrees. Who is correct? Justify your conclusion.
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15 un2 15 un2 15 un2
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Area of Parallelogram
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b. Does the angle at which the parallelogram slants matter? Why or why not? Explain how you know.
No, the base is the same and the height is always perpendicular
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A = bhParallelogram
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6.3 – AREA OF PARALLELOGRAMS, CONT.Several more parallelograms are shown below. In each case, find a related rectangle for which you know both the base and height. Rotating your packet might help. Use what you know about rectangles to find the area of each parallelogram.
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A = bhA = (9)(4)A = 36un2
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A = bhA = (20)(5)A = 100un2
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A = bhA = (7)(3)A = 21un2
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Definition: If a quadrilateral is a parallelogram, then
both pairs of ________________ sides are ______________.
oppositeparallel
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If a quadrilateral is a parallelogram, then
both pairs of ________________ sides are
______________.
oppositecongruent
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If a quadrilateral is a parallelogram, then
both pairs of ________________ angles
are ________________.
oppositecongruent
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If a quadrilateral is a parallelogram, then
both pairs of _______________ angles are
___________________.
consecutive
supplementary
x y
xy
x y 180
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If a quadrilateral is a parallelogram, thenthe diagonals _______________ each other.bisect
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6.5 –PARALLELOGRAM PARTSFind the value of each variable in the parallelogram.
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a – 3 = 14a = 17
b + 2 = 7b = 5
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3x + 6 = 12
2y + 9 = 272y = 18
3x = 6x = 2
y = 9
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130°
50°
50°
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9b – 2 = 1069b = 108
b = 12
7a – 3 + 106 = 1807a + 103 = 180
a = 117a = 77
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If opposite sides of a quadrilateral are
________________, then the quadrilateral is a
________________.
congruent
parallelogram
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If both pairs of opposite angles are
_________________, then the quadrilateral is
a _________________.
congruent
parallelogram
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If consecutive angles are ________________,
then the quadrilateral is a ________________.
supplementary
parallelogram
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If the diagonals ____________ each other,
then the quadrilateral is a ________________.
bisect
parallelogram
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If one pair of opposite sides are ____________
and ____________, then the quadrilateral is a
________________.
congruent
parallelogram
parallel
New!!!
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6.6 –PROVING PARALLELOGRAMSCan you prove the quadrilaterals are parallelograms? Why or why not?
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yesOne pair of opposite sides parallel and congruent
yesBoth pairs of opposite angles are congruent
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noParallel and congruent marks are not on the same sides.
yesBoth pairs of opposite sides are congruent
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yesBoth pairs of opposite sides are parallel
noOnly one pair of congruent angles
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yesDiagonals bisect each other
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6.7 –PARALLELOGRAM IDENTIFICATIONThe definition of a parallelogram is, "A quadrilateral with both opposite sides parallel." Based on this definition, circle all parallelograms below.
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AB
CD
a. What is the slopes of all four line segments?
AB = ______ BC = ______
CD = ______ AD = ______
27
27
8
1
81
27
81
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AB
CD
b. What is the relationship between these sides, given the slopes? Explain.
AB = ______ BC = ______
CD = ______ AD = ______
27
27
A
8
1
81
27
81
Both opposite sides are parallel
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AB
CD
c. What is the length of all four line segments?
AB = ______ BC = ______
CD = ______ AD = ______
27
A
8
1
22 + 72 = d2
4 + 49 = d2
53 = d2
5312 + 82 = d2
1 + 64 = d2
65 = d2
65
53 65
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AB
CD
d. What is the relationship between these sides, given their length? Explain.
AB = ______ BC = ______
CD = ______ AD = ______
27
A
8
1
53 65
53 65
Both opposite sides are congruent
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AB
CD
e. What kind of quadrilateral is this? How do you know?
27
A
8
1
Parallelogram, Both opposite sides are parallel and congruent
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Parallelogram
Rectangle
Rhombus
Square
Trapezoid
IsoscelesTrapezoid
Kite
Triangle
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NameBlock #
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Parallelogram
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• Both opposite sides parallel
• Both opposite sides congruent• Both opposite angles congruent
• Consecutive angles supplementary
• Diagonals bisect each other
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A bh
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Triangle
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• 3 sides
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12
A bh