1. What do you notice about the construction of this building - the Rock and Roll Hall of Fame and Museum?

2. Notice the parts of the building highlighted here
Notice the parts of the building highlighted here? What might you be able to say about them?

3. Midsegment Theorem
Unit 5.1

4. 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.

5. What is a midsegment?
A midsegment is a segment that connects the midpoints of two sides of a triangle.

6. A B C M N
Label triangle ABC and midpoints M & N.
Measure BMN, & BAC.
Record your measures.
Compare your results to others.
Make a conjecture about
Conjecture:

7. Conjecture:
The segment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle.

8. Measure MN & AC with a ruler.B C M N
Make a conjecture about the
length of MN with respect to
the length of AC.
Conjecture: MN is ½ of AC

9. Theorem
The midsegment is parallel to the side of a triangle and is half the length of that side.
7 in.
14 in.

10. Measure the midpoint of AC Label this point P.
Connect point P to M.
Connect point P to N.
Fold on
(or cut triangles apart and compare)
Make a conjecture about the four small triangles.

11. If you cut the original triangle on the midsegments, it creates 4 congruent triangles.

12. She wants to decorate the midsegments with red ribbon.
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)

13. Finding the midsegment on a graph.y x
(2,1)
(5,5)
(12,1)
Locate these endpoints
To locate the midsegment of a triangle on a graph, you need to use the midpoint formula to find the endpoints of the midsegment.
5+2 , 5+1
(3.5, 3)
(note: This is only one endpoint)

14. 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.

15. Practice
Find the midsegments, and their lengths, of the triangle with these verticies.
A (1,3)
B (5,6)
C (9,3)

16. HOMEWORK
Similarity 5 Worksheet