1. 5-3 & 5-4: Midsegments and Medians of Triangles
Rigor: Identify and apply theorems about medians and midsegments.
Relevance: center of gravity and indirect measurement

2. Triangle Midsegment Theorem
Midsegment Definition: The midsegment of a triangle connects the midpoints of 2 sides.
Theorem: The midsegment of a triangle is half the length of the side it is parallel to.

3. Example 1: Indirect Measurement
Calculate the distance across the base of the volcano and across the sink hole.
775m

4. Example 2: Calculate each measureUW
mUWT RT . .

5. Example 3: Coordinate Geometry

6. Example 4: Calculate the value of n

7. 5-4 Assignment
Workbook pg 214 ALL

8. Medians and Centroids
Median of a triangle – the segment from the vertex to the midpoint of the opposite side.
Centroid – the point of concurrency of the 3 medians
Always inside the triangle
FUN FACT! The centroid is also known as the triangle’s center of gravity because you could balance any triangular object from its centroid!

9. Ex 5: Center of Gravity
Below are plans for a triangular piece of a mobile. Where should the support be attached so the mobile is balanced?

10. The Centroid Theorem Vertex to centroid = 2/3 length of median
Midpoint to centroid = 1/3 length of median
The small piece is 1/2 the length of the medium piece.
Easiest place to start is to find 1/3 of the median (the small piece)

11. EX 6: Calculate the missing lengths
RS = 7. What is SL & RL?
NQ = 18. What is NS & SQ?
MS= 10. What is SP & MP?

12. 5- 3 Assignment Workbook pg 209 #1 – 4 Honors also do #8 – 9
Workbook pg 210 #1 and 5
Honors also do #6