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
6.1
What If Both Sides Are Parallel?Pg. 4
Parallelograms
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?
6.1 –PARALLELOGRAMSFind the areas of the figures below. Can you find more than one method for finding the area?
2 4 2
8 un2
4
12
4
20 un2
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.
a. Keesha thinks that the rectangle and parallelograms below have the same area. Her teammate Saundra disagrees. Who is correct? Justify your conclusion.
15 un2 15 un2 15 un2
Area of Parallelogram
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
A = bhParallelogram
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.
A = bhA = (9)(4)A = 36un2
A = bhA = (20)(5)A = 100un2
A = bhA = (7)(3)A = 21un2
Definition: If a quadrilateral is a parallelogram, then
both pairs of ________________ sides are ______________.
oppositeparallel
If a quadrilateral is a parallelogram, then
both pairs of ________________ sides are
______________.
oppositecongruent
If a quadrilateral is a parallelogram, then
both pairs of ________________ angles
are ________________.
oppositecongruent
If a quadrilateral is a parallelogram, then
both pairs of _______________ angles are
___________________.
consecutive
supplementary
x y
xy
x y 180
If a quadrilateral is a parallelogram, thenthe diagonals _______________ each other.bisect
6.5 –PARALLELOGRAM PARTSFind the value of each variable in the parallelogram.
a – 3 = 14a = 17
b + 2 = 7b = 5
3x + 6 = 12
2y + 9 = 272y = 18
3x = 6x = 2
y = 9
130°
50°
50°
9b – 2 = 1069b = 108
b = 12
7a – 3 + 106 = 1807a + 103 = 180
a = 117a = 77
If opposite sides of a quadrilateral are
________________, then the quadrilateral is a
________________.
congruent
parallelogram
If both pairs of opposite angles are
_________________, then the quadrilateral is
a _________________.
congruent
parallelogram
If consecutive angles are ________________,
then the quadrilateral is a ________________.
supplementary
parallelogram
If the diagonals ____________ each other,
then the quadrilateral is a ________________.
bisect
parallelogram
If one pair of opposite sides are ____________
and ____________, then the quadrilateral is a
________________.
congruent
parallelogram
parallel
New!!!
6.6 –PROVING PARALLELOGRAMSCan you prove the quadrilaterals are parallelograms? Why or why not?
yesOne pair of opposite sides parallel and congruent
yesBoth pairs of opposite angles are congruent
noParallel and congruent marks are not on the same sides.
yesBoth pairs of opposite sides are congruent
yesBoth pairs of opposite sides are parallel
noOnly one pair of congruent angles
yesDiagonals bisect each other
6.7 –PARALLELOGRAM IDENTIFICATIONThe definition of a parallelogram is, "A quadrilateral with both opposite sides parallel." Based on this definition, circle all parallelograms below.
AB
CD
a. What is the slopes of all four line segments?
AB = ______ BC = ______
CD = ______ AD = ______
27
27
8
1
81
27
81
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
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
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
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
Parallelogram
Rectangle
Rhombus
Square
Trapezoid
IsoscelesTrapezoid
Kite
Triangle
NameBlock #
Parallelogram
• Both opposite sides parallel
• Both opposite sides congruent• Both opposite angles congruent
• Consecutive angles supplementary
• Diagonals bisect each other
A bh
Triangle
• 3 sides
12
A bh
