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Transcript Document

What do you notice
about the construction
of this building - the
Rock and Roll Hall of
Fame and Museum?
http://www.rockhall.com/museum/about.asp
Notice the parts of the
building highlighted
here? What might you
be able to say about
them?
Midsegment Theorem
Unit 5.1
INVESTIGATION 5.1
Draw a large triangle on paper, measure to locate midpoints of
two sides of the triangle, draw in the segment connecting the
two midpoints.
(midpoint)
(midpoint)
This segment is called a midsegment.
What is a midsegment?
A midsegment
is a segment
that connects
the midpoints
of two sides
of a triangle.
B
M
A
Label triangle ABC and midpoints M & N.
Measure BMN, & BAC.
Record your measures.
Compare your results to others.
Make a conjecture about MNand AC
Conjecture:
MN AC
N
C
Conjecture:
The segment
connecting the
midpoints of
two sides of a
triangle is
parallel to the
third side of the
triangle.
Measure MN & AC with a ruler.
Make a conjecture about the
length of MN with respect to
the length of AC.
M
A
Conjecture: MN is ½ of AC
B
N
C
Theorem
The
midsegment
is parallel to
the side of a
triangle and
is half the
length of
that side.
7 in.
14 in.
Measure the midpoint of AC
Label this point P.
Connect point P to M.
Connect point P to N.
B
M
A
P
MN
,
PM
,&
PN
.
Fold on
(or cut triangles apart and compare)
N
C
Make a conjecture about the four small triangles.
If you cut the
original triangle on
the midsegments, it
creates 4 congruent
triangles.
Sadie is designing
a kite. The diagonals
Measure 64 cm and 90 cm.
She wants to decorate the
midsegments with red ribbon.
How much ribbon must she purchase?
(Answer: 154 cm)
Finding the midsegment on a graph.
y
(5,5)
(12,1)
(2,1)
x
Locate these endpoints
5+2 , 5+1
2
2
(3.5, 3)
(note: This is only one endpoint)
To locate the
midsegment of a
triangle on a
graph, you need
to use the
midpoint
formula to find
the endpoints of
the midsegment.
Length
You can also use the distance formula
to find the length of either the side of a
triangle or the length of a midsegment.
d ( x2 x1 ) ( y2 y1 )
2
2
Practice
Find the midsegments, and their
lengths, of the triangle with these
verticies.
A (1,3)
B (5,6)
C (9,3)
HOMEWORK
Similarity 5 Worksheet