5.1 Midsegment Theorem and Coordinate Proof
Goal  Use properties of midsegments and write coordinate proofs.
Day 1:
VOCABULARY
Midsegment of a triangle
________________________________________________________________________
________________________________________________________________________
Coordinate proof
________________________________________________________________________
________________________________________________________________________
THEOREM 5.1: MIDSEGMENT THEOREM
The segment connecting the midpoints of two sides of a triangle is __________ to the third side and is ______
as long as that side.
Example 1
Use the Midsegment Theorem to find lengths
Windows A large triangular window is segmented as shown. In the diagram, DF and EF are midsegments of
ABC. Find DF and AB.
Checkpoint
1.
In Example 1, consider ADF. What is the length of the midsegment opposite DF ?
_________________________________________________________________
_________________________________________________________________
Example 2
Use the Midsegment Theorem
In the diagram at the right, QS = SP and PT = TR. Show that QR  ST .
S
2. In Example 2, if V is the midpoint of QR , what do you know about SV ?
Extra Practice:
MP a midsegment of LNO. Find the value of x.
1
3.
2.
4.
In DEF, EJ  JF , KF  FD and DG  GE . Copy and complete the statement.
5.
6.
7.
8.
GJ ║__?__
EJ __?__  __?__
DE ║ __?__
GJ  __?__  __?__
Example 3
Place a figure in a coordinate plane
Place each figure in a coordinate plane in a way that is convenient for finding side lengths. Assign
coordinates to each vertex.
a. a square
b. an acute triangle
Example 4
Apply variable coordinates
In Example 3 part (a), find the length and midpoint of a diagonal of the square.
Extra Practice
Use the graph shown.
1.
Find the coordinates of the endpoints of each midsegment of PQR.
Place the figure in a coordinate plane. Assign coordinates to each vertex.
2. A 4 unit by 7 unit rectangle with one vertex at (0, 0).
3. A square with side length s and one vertex at (s, 0).
Hmwrk: pg 298 1, 3-11 all 12,14, 47,48,50,51,52