Transcript 8.2 Use Properties of Parallelograms

Assignment
• P. 518-521: 1, 2, 416 even, 24, 26,
28-33, 39, 40, 42,
43, 46-48
• P. 723-724: 1, 3, 4,
10, 11, 17, 23, 24,
26, 36
• Challenge
Problems
Parallelograms
What makes a polygon a parallelogram?
8.2 Use Properties of Parallelograms
Objectives:
1. To discover and use properties of
parallelograms
2. To find side, angle, and diagonal
measures of parallelograms
3. To find the area of parallelograms
The Story of Parallelograms
For this lesson, we’ll be writing The Story of
Parallelograms. While short on plot, the
story is definitive and is illustrated. In
order to write this book, we’ll need to make
a small, 8-page booklet with no staples.
That part is magic.
The Story of Parallelograms: Page Layout
1. Title
2. Definition
3. Picture
4. Theorem 1
5. Theorem 2
6. Theorem 3
7. Theorem 4
8. Area
Parallelogram
A parallelogram is a
quadrilateral with
both pairs of
opposite sides
parallel.
• Written PQRS
• PQ||RS and QR||PS
Investigation 1
In this Investigation, we
will be using
Geometer’s
Sketchpad to
construct a perfect
parallelogram, and
then we will discover
four useful properties
about parallelograms.
Theorem 1
If a quadrilateral is a
parallelogram, then
its opposite sides
are congruent.
If PQRS is a parallelogram, then PQ  RS and QR  PS.
Theorem 2
If a quadrilateral is a
parallelogram, then
its opposite angles
are congruent.
If PQRS is a parallelogram, then P  R and Q  S .
Theorem 3
If a quadrilateral is a
parallelogram, then
consecutive angles
are supplementary.
If PQRS is a parallelogram, then x + y = 180°.
Theorem 4
If a quadrilateral is a
parallelogram, then
its diagonals bisect
each other.
Example 1
Find each indicated measure.
1. NM
2. KM
3. mJKL
4. mLKM
Example 2
The diagonals of
parallelogram
LMNO
intersect at
point P. What
are the
coordinates of
P?
Example 3
Find the values of c and d.
Example 4
For the parallelogram below, find the values
of t and v.
Example 5: SAT
For parallelogram ABCD, if AB > BD, which
of the following statements must be true?
I. CD < BD
II. ADB > C
III. CBD > A
B
A
C
D
Bases and Heights
Any one of the sides of a parallelogram can
be considered a base. But the height of a
parallelogram is not necessarily the length
of a side.
Bases and Heights
The altitude is any segment from one side of
the parallelogram perpendicular to a line
through the opposite side. The length of
the altitude is the height.
Bases and Heights 2
The altitude is any segment from one side of
the parallelogram perpendicular to a line
through the opposite side. The length of
the altitude is the height.
Investigation 2
Now you will discover
a formula for
computing the area
of a parallelogram.
Area of a Parallelogram Theorem
The area of a parallelogram is the product of
a base and its corresponding height.
A = bh
Height (h)
Height (h)
Base (b)
Base (b)
Area of a Parallelogram Theorem
The area of a parallelogram is the product of
a base and its corresponding height.
A = bh
Example 6
Find the area of parallelogram PQRS.
Example 7
What is the height of
a parallelogram that
has an area of 7.13
m2 and a base 2.3
m long?
Example 8
Find the area of each triangle or parallelogram.
1.
2.
3.
Example 9
Find the area of the parallelogram.
Assignment
• P. 518-521: 1, 2, 416 even, 24, 26,
28-33, 39, 40, 42,
43, 46-48
• P. 723-724: 1, 3, 4,
10, 11, 17, 23, 24,
26, 36
• Challenge
Problems