how do I solve it Concurrent Lines For use after Section 103

how do I solve it

Concurrent Lines For use after Section 10-3 The medians of ABC are shown. Complete. 1. If BE 18, then BH 2. If AG = 10.5, then AH 3. If FH = 4, then CH and HE = --, and HG = and CF- Exs. 1-3

Solution

Point H is the known as the centroid, the point of intersection of the 3 medians. The property of the centroid is that divides each median in the ratio 2:1 (Vertex to centroid/Centroid to base = 2/1).

Therefore CH/HF = BH/HE = AH/HG = 2/1. So the numerator (vertex to centroid) = 2/3 of the median length and the denominator ( centroid to base) = 1/3 of median length.

1) BE = 18, then BH = 2/3 * 18 = 12 and HE = 1/3 * 18 = 6

2) AG = 10.5, then AH = 2/3 * 10.5 = 7 and HE = 1/3 * 10.5 = 3.5

3) FH = 1/3 of median length = 4.

Therefore median length CF = 4 * 3 = 12 and

CH = 2/3 * 12 = 8