1. Warm up: Calculate midsegments
TODAY IN GEOMETRY…
Warm up: Calculate midsegments
Learning Target: 5.4 Identify the Medians of Triangles and the Centroid
Independent Practice
Mini Quiz – Friday!
ALL HW due Friday!

2. WARM UP: Complete the statement: 1. 𝑅𝑆 ∥ 2. 𝑆𝑇 ∥ 3. 𝐾𝐿 ∥ 4. 𝑆𝐿 ≅ ≅
1. 𝑅𝑆 ∥
2. 𝑆𝑇 ∥
3. 𝐾𝐿 ∥
4. 𝑆𝐿 ≅ ≅
5. 𝐽𝑅 ≅ ≅
6. 𝐽𝑇 ≅ ≅ 𝐾 𝐽𝐿 𝐽𝐾 𝑅 𝑆 𝑅𝑇 𝐾𝑆 𝑅𝑇 𝐿 𝐽 𝑇 𝐾𝑅 𝑆𝑇 𝐿𝑇 𝑅𝑆

3. MEDIAN OF A TRIANGLE: A segment from a vertex to the midpoint of the opposite side.
Find the midpoint on one segment.
Draw a line from the opposite vertex through the midpoint.
vertex
median
midpoint

4. The three medians of a triangle are concurrent
The three medians of a triangle are concurrent. The point of concurrency is called the CENTROID and falls inside the circle. The centroid is the balancing point of a triangle.
Find the medians for each side of the triangle.
CENTRIOD

5. A different way to think about this:
CONCURRENCY OF MEDIANS: The medians of a triangle intersect at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side.
𝐴𝑃= 2 3 𝐴𝐵 𝐴
A different way to think about this:
𝐴𝑃 is twice as long as 𝐵𝑃 OR
𝐵𝑃 is half of 𝐴𝑃 𝟐𝒙 𝑃 𝒙 𝐵
CENTRIOD

6. PRACTICE: 𝑃 is the centroid of △𝐴𝐷𝐸, 𝐶𝐸=27𝐵 𝐶 𝐸 𝐹
1. 𝐹𝐸=
2. 𝐶𝑃=
3. 𝑃𝐸=
4. 𝐹𝑃=
5. 𝐹𝐷=
6. 𝐴𝐸=
𝐴𝐹=12 12
1 3 𝐶𝐸=9
2 3 𝐶𝐸=18
1 2 𝐷𝑃=3 6
𝐹𝑃+𝑃𝐷=9
2𝐴𝐹=24

7. PRACTICE: 𝐺 is the centroid of △𝐴𝐵𝐶. Find x.
1. 𝐶𝐺=3𝑥+7 𝑎𝑛𝑑 𝐶𝐸=6𝑥
𝐶𝐺= 2 3 𝐶𝐸
3𝑥+7= 2 3 (6𝑥)
3𝑥+7=4𝑥
− 3𝑥 − 3𝑥
𝟕=𝒙
2. 𝐹𝐺=𝑥+8 𝑎𝑛𝑑 𝐴𝐹=9𝑥−6
𝐹𝐺= 1 3 𝐴𝐹
𝑥+8= 1 3 (9𝑥−6)
𝑥+8=3𝑥−2
− 𝑥 − 𝑥
8=2𝑥−2
10=2𝑥 𝐴 𝐵 𝐺 𝐷 𝐸 𝐶 𝐹
𝟓=𝒙

8. PRACTICE: Find the midpoint 𝑀 of 𝐴𝐸 then draw the median
PRACTICE: Find the midpoint 𝑀 of 𝐴𝐸 then draw the median. Use the median 𝐴𝑀 to find the coordinates of the centroid.
Midpoint Formula 𝑀( 𝑥 1 + 𝑥 2 2 , 𝑦 1 + 𝑦 2 2 )
Substitute Values , 7+1 2
Add and Divide (7, 4)
Connect the midpoint 𝑀 to vertex 𝐶
Centroid is 𝐶𝑀= =6
Count 6 units down from the vertex 𝐶
Centroid is (7, 7)
𝐶(7, 13) 𝟗
(7, 7)
𝐴(3, 7)
𝑀(7 4)
𝐸(11, 1)

9. HOMEWORK #2:
Pg. 322: 3-11, 33-35
If finished, work on other assignments:
HW #1: Pg. 298: 3-15, 24-27