A segment that connects a vertex of a triangle

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Date: Sec 5-4 Concept: Medians and Altitudes of a Triangle

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Presentation transcript:

A segment that connects a vertex of a triangle to the midpoint of the opposite side. The point of concurrency of the medians of a triangle. The perpendicular segment from a vertex of a triangle to the opposite side. The point of concurrency of the altitudes of a triangle.

AE BF CD Also, EP = 1/3AE, FP = 1/3BF, and DP = 1/3CD Therefore, AP = 2EP, BP = 2FP, and CP = 2DP

GM 2/3 6 2/3 6 9 3/2 GM 9 6 3 3 6

FM = 2/3FK 10 = 2/3FK 15 = FK MK = 1/2FM MK = 1/2(10) MK = 5

1 + 7 2 + 4 (4, 3) two thirds 3 3 2/3 3 2 2 4, 4 If you don't have a horizontal or vertical line as a median you would have to use the distance formula to find the length of the median, then take 2/3 of the length to find the centroid.

concurrent

Orthocenter Orthocenter

Point K should be moved to (4, 9)

∠ADB ∠CDB Altitude HL Congruence Theorem CD Midpoint

AB ≅ CB Given ∠ADB ≅ ∠CDB All right ∠'s are ≅ BD ≅ BD Reflexive Property ∆ABD ≅ ∆CBD HL ≅ Thm ∠ABD ≅ ∠CBD CPCTC BD is an ∠ bisector Definition of bisector Statements Reasons