Download Revised Geometry Lesson 6.3

6.3 Properties of Parallelograms
Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
n
3
4
5
6
7
8
9
n-2
1
2
3
4
5
6
7
Sum of angles
180 degrees
720 degrees
6.3 Properties of
Parallelograms
• Goal #1:
• How to use
properties of
parallelograms to
solve problems in
geometry.
• Goal #2:
• How to use
properties of
parallelograms to
solve real life
problems.
6.3 Properties of
Parallelograms
Power Standard #8
Understand the properties, characteristics, and
notation of geometric figures/solids to determine
how they relate to one another. (1.3.2)
[1.2, 6.1-6.3, 6.5, 6.6]
Parallelogram
• A parallelogram is a quadrilateral whose
opposite sides are parallel.
Lesson Investigation
Part A - Instructions
• In pairs, use a straightedge to draw two parallel
segments on a piece of patty paper. Then draw two
other parallel segments to form a parallelogram.
• Place a second piece of patty paper over the first and
copy the parallelogram onto the second.
• By moving the copies around, what conjectures can you
make about the properties of parallelograms.
• You have ten minutes!!!
Part A – Guiding Questions
• How do the lengths of the opposite sides compare?
• How do the sizes of the opposite angles compare?
• How do the sizes of consecutive angles compare?
Parallelogram
Part A – Guiding Questions
• How do the lengths of the opposite sides compare?
• How do the sizes of the opposite angles compare?
• How do the sizes of consecutive angles compare?
Lesson Investigation
Part B – Instructions
• Draw or fold the two diagonals of the parallelogram.
• Place a dot at their intersection.
• You have five minutes!!!
Part B - Guiding Questions
• How do the segments of each diagonal compare?
• What can be said about the intersection of the
diagonals?
• How many congruent triangles are formed within the
parallelogram?
Parallelogram
Part B - Guiding Questions
• How do the segments of each diagonal compare?
• What can be said about the intersection of the diagonals?
• How many congruent triangles are formed within the parallelogram?
Properties of Parallelograms
• THM 6.3: The opposite sides of a
parallelogram are congruent.
• THM 6.4: The opposite angles of a
parallelogram are congruent.
Properties of Parallelograms
• THM 6.5: The consecutive interior
angles of a parallelogram are
1
supplementary.
m1  m2  180
2
THM 6.6: The diagonals of a parallelogram
bisect each other.
Find SR, ST , mPQR, mQRS ,
if PQRS is a
ogram and mQPS  110
P
5
110
C. m PQR  70
D. m QRS  110
3
70
T
3
A. SR  PQ  5
B. ST  QT  3
Q
110
S
5
R
Using Parallelograms to solve
Real life problems
• The San Francisco
Bay Bridge, like
many bridges, uses
parallelograms in its
structural design.
• Engineers use
properties of
parallelograms to
build and repair
bridges.
The framework for a railroad bridge is shown below.
____
____
____
____
You know only that ED BC, AB EF , and m PER  130.
130
A.
Are you given enough info to verify that EQ = QB? Yes!
B.
What are the measures of
ERB and
RBP?
50
130
Assignment!!!
•
•
•
•
Pg. 283
11-23 odd,
27b-36 even,
42, 44.