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5.3 Medians and Altitudes of a Triangle

Objective: SWBAT use the properties of altitudes and medians of a triangle. 5.3 Medians and Altitudes of a Triangle. Definitions. Median of a Triangle – a segment that starts at a vertex and ends at the midpoint of the opposite side of a triangle.

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5.3 Medians and Altitudes of a Triangle

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  1. Objective: SWBAT use the properties of altitudes and medians of a triangle. 5.3 Medians and Altitudes of a Triangle

  2. Definitions • Median of a Triangle – a segment that starts at a vertex and ends at the midpoint of the opposite side of a triangle. • Concurrent – when three or more lines intersect at one point. • Centroid (of a triangle) – the point where the three medians of a triangle meet • * The medians are concurrent

  3. Concurrency of Medians of a Triangle (Theorem)‏ • The medians intersect at a point which is 2/3 the length of each median • AG = 2/3 AD, CG = 2/3 CF, BG = 2/3 BE

  4. Example • If PT = 6, what is PR? • If RV = 3, what is NV? • PR = 2/3 PT • PR = 2/3 (6)‏ • PR = 4 • RV = 2/3 NV • 3 = 2/3 NV • 3 (3/2) = NV divide by 2/3 or multiply by 3/2 • 4.5 = NV

  5. Altitudes • Altitude of a triangle – the perpendicular segment which begins begins at a vertex and ends on the opposite side of a triangle (altitudes may lie outside triangle). • Orthocenter of a triangle – the point where the 3 altitudes meet. • *Altitudes are concurrent • The orthocenter is on a right triangle • The orthocenter is in an acute triangle • The orthocenter is outside an obtuse triangle

  6. Assignment • p. 282-283 1-23 (skip 12,19)‏ • *On 13-16, draw triangle & use a ruler

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