lesson 12 – points of concurrency ii. page 53 the point of concurrency of the medians is known as...
TRANSCRIPT
UNIT 3Lesson 12 – Points of Concurrency II
Page 53
The point of concurrency of the medians is known as the centroid which is the center of gravity.
Page 54
Angle bisectorsCuts an angle
into two congruent angles
Always inside of the triangle
Medians
Joins the midpoint of the
side of a triangle with its opposite
vertex
Always inside of the triangle
Altitudes
Segment joining the vertex of a triangle to the opposite side
Both; depends on the type of
triangle
Page 54
Circumcenter and Orthocenter
They are both related to perpendicular segments
Page 55
𝑥 𝑦𝑧
𝐶𝐹=2𝑥 ,𝐵𝐹=2 𝑧 , 𝐴𝐹=2 𝑦
Page 56
4
𝑦
1610
¿8
¿8
¿20
Page 56
2 ( 𝑋+3 )=5 𝑋−92 𝑋+6=5 𝑋−9−2 𝑋−2 𝑋
6=3 𝑋 −9+9+915=3 𝑋33
5=𝑋
𝐸𝐹=𝑥+3𝐸𝐹=5+3𝐸𝐹=8
Page 56
𝐷𝐹𝑎𝑛𝑑𝐶𝐹𝑎𝑟𝑒 𝑖𝑛𝑎𝑟𝑎𝑡𝑖𝑜1 :2𝑆𝑜 , 𝑙𝑒𝑡 𝐷𝐹=1 𝑥𝑎𝑛𝑑𝐶𝐹=2 𝑥
𝑥+2𝑥=153 𝑥=1533𝑥=5
𝐷𝐹=5𝑎𝑛𝑑𝐶𝐹=10
Page 57
Angle bisectors
8442 42
28
∡𝐵𝑅𝐶+42+28=180∡𝐵𝑅𝐶+70=180
−70−70∡𝐵𝑅𝐶=110
Homework – Page 58