Medians.

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Presentation transcript:

Medians

Median Median Connect the vertex to the opposite side's midpoint

Who am I? Median

Perpendicular Bisector Who am I? Perpendicular Bisector

Who am I? Altitude

Who am I? Angle Bisector

Who am I? Altitude

Who am I? 20 Angle Bisector

Start to memorize… Indicate the special triangle segment based on its description

I connect the vertex to the opposite side’s midpoint Who am I? I connect the vertex to the opposite side’s midpoint Median

Special Property of Medians

How many medians does a triangle have? CENTROID:The intersection of all 3 Medians. The Centroid is also the Center of Gravity

Vertex to CENTROID is TWICE as much as CENTROID to MIDPOINT Theorem Vertex to CENTROID is TWICE as much as CENTROID to MIDPOINT 2x x

C How much is CX? D CX = 2(XF) E X CX = 2(13) 13 B A F CX = 26

C How much is XD? D AX = 2(XD) E X 18 18 = 2(XD) B A F 9 = XD

In ABC, AN, BP, and CM are medians. Ex: 1 In ABC, AN, BP, and CM are medians. C If EM = 3, find EC. N EC = 2(3) P E EC = 6 B M A

In ABC, AN, BP, and CM are medians. Ex: 2 In ABC, AN, BP, and CM are medians. C If EN = 12, find AN. N AE = 2(12)=24 P E B AN = AE + EN M A AN = 24 + 12 AN = 36

EB =22 2(3x+2)=8x-2 If PE = 3x+2, find EB=7x-1 C Find EB. N If PE = 3x+2, find EB=7x-1 Find EB. C N 2 times small = big P E 2(3x+2)=8x-2 B M A EB =22