Objective: Learn to identify the medians in a triangle.

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Presentation transcript:

Objective: Learn to identify the medians in a triangle. Applied Geometry Lesson: 6 – 1 Medians Objective: Learn to identify the medians in a triangle.

Median A segment that joins a vertex of the triangle and the midpoint of the side opposite that vertex.

EG = 2(EN) 11 = 2(EN) 5.5 = EN

NP = 2(NC) 9 = NC 18 = 2(NC) MP = 2(DP) MP = 15 MP = 2(7.5)

SP = 5x - 4 RQ = QT SP = 5(10) - 4 7x – 1= 6x + 9 SP = 46 x – 1= 9 PT = SP x = 10 PT = 46

CD = BD 3 = x AE = 5(3) - 2 2x + 5 = 4x - 1 AE = 13 5 = 2x - 1 BE = 13 6 = 2x

How many medians can you have in one triangle? 3 (one from each vertex) Centroid The point where the medians of a triangle intersect. Concurrent When three or more lines or segments meet at the same point.

Centroid The length of the segment from the vertex to the centroid is twice the length of the segment from the centroid to the midpoint.

x 2x ZQ = 2(QN) ZQ = 2(5) ZQ = 10

x 2x

DG = 7 BG = 2(GF) BF = 6.8 + 13.6 BG = 2(6.8) BF = 20.4 BG = 13.6

Homework Pg. 231 1 – 7 all, 8 – 28 E