1. Warm Up Given: AM = BM Prove:<AMP = <BMO 1.Circle O1. Given 2.AM = BM2. Given 3.MO = MO3. Reflexive Prop 4.Draw AO and BO4. Two points determine a segment 5.AO = BO5. All radii of a circle are congruent 6. ΔAMO = ΔBMO6. SSS 7. <AMO = <BMO7. CPCTC

2. 3.4 Beyond CPCTC Medians: Every triangle has 3 medians A median is a line segment drawn from any vertex to the midpoint of its opposite side. A median bisects the segment.

3. A B F E C D Name the 3 medians of triangle ABC.

4. Altitudes: Every triangle has 3 altitudes. An altitude is a line segment drawn perpendicular from any vertex to its opposite side. *The altitude could be drawn outside the triangle to be perpendicular. Altitudes form right angles 90˚ You may need to use auxiliary lines (lines added)

5. Could an altitude also be a median? Yes, for an isosceles triangle when drawn from the vertex.

6. Postulate: Two points determine a line, ray or segment. Determine (one and only one line)