5.4. Medians http://www.ck12.org
1
2
BH=HForBH= 2 HF HC=2
3
DCor3
2
HC=DC
3 x+ 6 = 2 ( 2 x− 1 )3
2
( 2 y+ 8 ) = 5 y− 16
3 x+ 6 = 4 x− 2 3 y+ 12 = 5 y− 16
8 =x 28 = 2 y- This statement is true. By definition, a median intersects a side of a triangle at its midpoint. Midpoints divide
segments into two equal parts.
Interactive Practice
MEDIA
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URL: http://www.ck12.org/flx/render/embeddedobject/113026Explore More
For questions 1-4, find the equation of each median, from vertexAto the opposite side,BC.
1.A( 9 , 5 ),B( 2 , 5 ),C( 4 , 1 )
2.A(− 2 , 3 ),B(− 3 ,− 7 ),C( 5 ,− 5 )
3.A(− 1 , 5 ),B( 0 ,− 1 ),C( 6 , 3 )
4.A( 6 ,− 3 ),B(− 5 ,− 4 ),C(− 1 ,− 8 )For questions 5-9,B,D, andFare the midpoints of each side andGis the centroid. Find the following lengths.
- IfBG=5, findGEandBE
- IfCG=16, findGFandCF
- IfAD=30, findAGandGD
- IfGF=x, findGCandCF
- IfAG= 9 xandGD= 5 x−1, findxandAD.
Use 4 ABCwithA(− 2 , 9 ),B( 6 , 1 )andC(− 4 ,− 7 )for questions 10-15.