1. Lesson 12 – Points of Concurrency II
Unit 3
Lesson 12 – Points of Concurrency II

2. Page 53
The point of concurrency of the medians is known as the centroid which is the center of gravity.

3. Cuts an angle into two congruent angles Always inside of the triangle
Page 54
Cuts an angle into two congruent angles
Always inside of the triangle
Angle bisectors
Joins the midpoint of the side of a triangle with its opposite vertex
Always inside of the triangle
Medians
Segment joining the vertex of a triangle ⊥ to the opposite side
Both; depends on the type of triangle
Altitudes

4. Circumcenter and Orthocenter
Page 54
Circumcenter and Orthocenter
They are both related to perpendicular segments

5. Page 55 𝑥 𝑦 𝑧
𝐶𝐹=2𝑥, 𝐵𝐹=2𝑧, 𝐴𝐹=2𝑦

6. Page 56 =8 𝑦 =8 16 4 10
=20

7. Page 56
2 𝑋+3 =5𝑋−9
2𝑋+6=5𝑋−9
−2𝑋 −2𝑋
6=3𝑋−9
15=3𝑋
5 = 𝑋
𝐸𝐹=𝑥+3
𝐸𝐹=5+3
𝐸𝐹=8

8. Page 56
𝐷𝐹 𝑎𝑛𝑑 𝐶𝐹 𝑎𝑟𝑒 𝑖𝑛 𝑎 𝑟𝑎𝑡𝑖𝑜 1:2
𝑆𝑜, 𝑙𝑒𝑡 𝐷𝐹=1𝑥 𝑎𝑛𝑑 𝐶𝐹=2𝑥
𝑥+2𝑥=15
3𝑥=15
𝑥=5
𝐷𝐹=5 𝑎𝑛𝑑 𝐶𝐹=10

9. 84 Page 57 Angle bisectors 42 28 ∡𝐵𝑅𝐶+42+28=180 ∡𝐵𝑅𝐶+70=180 −70 −70
−70 −70
∡𝐵𝑅𝐶=110

10. Homework – Page 58