1. midsegment theorem OBJECTIVE: To use properties of midsegments to
solve problems
BIG IDEA: Coordinate Geometry
ESSENTIAL UNDERSTANDINGS:
To draw a midsegment, students must find the midpoint of two sides of a triangle and draw the segment joining the midpoints.
The midsegment of a triangle is related to the third side in two ways.
MATHEMATICAL PRACTICE: Make sense of problems and persevere in solving them

2. TERMS
Midsegment of a Triangle: a _______________ that connects the ____________________ of two sides of a triangle
Midsegments create a second triangle within the original triangle that is similar to the original triangle. They are parallel to their third sides, therefore the slopes are equal.
Midsegment Theorem: the _______________ connecting the ____________________ of two sides of a triangle is ____________________ to the _____________ side and is _______________ as long

3. TRIANGLE MIDSEGMENT
There are two special relationships between a midsegment of a triangle and the third side of the triangle C
D E
A F B
The perimeter of the triangle formed by the three midsegments of a triangle is half the perimeter of the original triangle

4. Example
EX 1: Show that the midsegment is parallel to and half as long.

5. Example
EX 2: are midsegments In Find
A E B
D F C

6. Examples EX 3: are midsegments in . Find the perimeter of X R Y T S Z
EX 4: Given , find the perimeter of

7. Example EX 5: The midpoints of the sides of a triangle are
a) What are the coordinates
of the vertices of the triangle?
b) Find the perimeter of
the triangle.

8. Example
EX 6: ENVIRONMENTAL SCIENCE A geologist wants to determine the distance, AB, across a sinkhole. Choosing a point E outside the sinkhole, she finds the distances AE and BE. She locates the midpoints C and D of and then measures What is the distance across the sinkhole?