Lesson 12 – Points of Concurrency II Unit 3 Lesson 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.

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

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

Page 55 𝑥 𝑦 𝑧 𝐶𝐹=2𝑥, 𝐵𝐹=2𝑧, 𝐴𝐹=2𝑦

Page 56 =8 𝑦 =8 16 4 10 =20

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

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

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

Homework – Page 58