1. 5.1 Midsegment Theorem & Coordinate Proof

2. Objectives
Use properties of midsegments
Understand coordinate proofs

3. Vocabulary
The Midsegment of a Triangle is a segment that connects the midpoints of two sides of the triangle. D B C E A
D and E are midpoints
DE is the midsegment

4. Midsegment Theorem Theorem 5.1
The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side. D B C E A
DE || AC
DE = ½ (AC)

5. Example 1 5 ft 16 ft TU = ________ PR = ________
In the diagram, ST and TU are midsegments of PQR. Find PR and TU.
5 ft
16 ft
TU = ________
PR = ________

6. Example 2 14 cm 53 cm ZY = ________ MN = ________
In the diagram, XZ and ZY are midsegments of LMN. Find MN and ZY.
14 cm
53 cm
ZY = ________
MN = ________

7. Example 3 x = ________ 10 DF = ________ 26 AB = ________ 52
In the diagram, ED and DF are midsegments of ABC. Find DF and AB.
3x – 4
5x + 2
x = ________ 10
DF = ________ 26
AB = ________ 52

8. Kinds of Proofs:
Two Column Proof has numbered statements and corresponding reasons that show an argument in a logical order.
A Flow Proof uses arrows to show the flow of a logical argument.
A Paragraph Proof presents a logical argument as a written explanation in paragraph form.
A Coordinate Proof is when you use variables to represent the coordinates of a generic figure to show the results are true for all figures of that type.

9. Example 4 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 rectangle b.
A scalene triangle
SOLUTION
It is easy to find lengths of horizontal and vertical segments and distances from (0, 0), so place one vertex at the origin and one or more sides on an axis.

10. Example 4 (continued) EXAMPL 3 a.
Let h represent the length and k represent the width. b.
Notice that you need to use three different variables.

11. Assignment
Workbooks Pg #1 – 18, 20