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
Definition: The midsegment of a triangle connects the midpoint 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.

4. Example 2: Calculate each measure. .

5. Example 3: Coordinate Geometry

6. Medians and Centroids
Median of a triangle – the segment from the vertex to the midpoint of the opposite side.
Centroid – where the medians intersect
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!

7. Concurrency of Medians Theorem
Vertex to centroid = 2/3 length of median
Midpoint to centroid = 1/3 length of median
Easiest place to start is to find 1/3 of the median

8. EX 4: Calculate the missing lengths
AB = 7. What is XA & XB?
CZ = 18. What is CA & AZ?
XA = 10. What is AB & XB?

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

10. 5- 3 & 5-4 Classwork Core book pg 209 #1 – 5 Core book pg 213 #1 – 9
You will be assigned HW on these sections in January.
Your homework this weekend is to complete the exam review. We will go over it on Monday.