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