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prove that median divides triangle into two equal parts

LET ABC BE THE TRIANGLE . AD IS THE MEDIAN.  IN TRIANGLE ABD AND ACD  AD =AD  (COMMON SIDE) ANGLE   ABD =ACD   (EACH IS 90)AB =AC     .THUS TRIANGLE ABD CONGRUENT TO ACD BY SAS CONGRUENCE. THIS IMPLIES MEDIAN DIVIDES A TRIANGLE INTO TWO EQUAL PARTS

  • -6
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Consider a triangle ABC Let D be the midpoint of overline{AB}, E be the midpoint of overline{BC}, F be the midpoint of overline{AC}, and O be the centroid.

By definition, AD=DB, AF=FC, BE=EC ,.File:Triangle.Centroid.Median.png Thus[ADO] = [BDO],[AFO] = [CFO],[BEO] = [CEO], and [ABE]=[ACE] ,, where [ABC] represents the area of triangle triangle ABC ; these hold because in each case the two triangles have bases of equal length and share a common altitude from the (extended) base, and a triangle's area equals one-half its base times its height.

We have:

[ABO]=[ABE]-[BEO] ,
[ACO]=[ACE]-[CEO] ,

Thus, [ABO]=[ACO] , and [ADO]=[DBO], [ADO]=frac{1}{2}[ABO]

Since [AFO]=[FCO], [AFO]= frac{1}{2}ACO=frac{1}{2}[ABO]=[ADO], therefore, [AFO]=[FCO]=[DBO]=[ADO],. Using the same method, you can show that [AFO]=[FCO]=[DBO]=[ADO]=[BEO]=[CEO] ,

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Manoj I don think your answer is possible as per ur explanation angle ABD=angle ACD=90 and they both are angles on the vertices of the triangle and a triangle cannot have 2 right angles  

  • -6

ABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = ½ AN x BD [1]

ar(ACD) = ½ AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal area.

  • 112

 hiii

  • -14

 ABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal area

  • 24

ABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal areaABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = � AN x BD [1]

ar(ACD) = � AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal area 

  • -27

Let ABC be a triangle and AD be it's median we have to prove that

ar(ABD)=ar(ACD)

ar(ABD)=1/2 * CD * AN

=1/2 *CD * AN

=ar (CD)

thus we can prove that median of a triangle divides it to 2 triangles of equal area

  • -18
Nice question
  • -10
show that the median of a triangle divides it into two triangle of equal area
  • -8
Here is the answer

  • -6
Draw a triangle ABC in which AD will be the median,means BD=CD
Construct AE perpendicular to BC.
To prove- Ar (ABD)=Ar (ACD)
Proof- Ar (ABD)=1/2*base*height
                        =1/2*AE*BD-(1)
Similarly,Ar (ACD)=1/2*AE*CD-(2)
According to given data-BD=CD
hence from(1)and(2)
Ar  (ABD)=Ar (ACD)
So it is proved that median divides it into two triangles of equal area
 
  • -1
Please find this answer

  • 12
ravinda mirinda
  • -2
hi
  • -14
hii
  • -13
Hello
  • -13
Here ABC is a triangle 
construction:join the median AD
now we get 2 right triangles such as ADB & ADC
consider the two triangles
from this,
AD=AD   common
AB=AC     sides
angle ADB=angle ADC=90 degree
 By RHS rule,
both triangles are congruent
 
  • -5

ABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = ½ AN x BD [1]

ar(ACD) = ½ AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal area.

  • -5
median
  • -3
yes
 
  • -6
ABC is the triangle and AD be the median (which means BD =DC). Construct AN perpendicular (90 degree) to BC. Now ar(ABD) = � AN x BD [1] ar(ACD) = � AN x CD [2] We know that BD=CD ( since AD is the median) Therefore ,from [1] and [2] ar ( ABD) = ar(ACD) => Median of a triangle divides it into two triangles of equal area
  • 3
dontno
  • 1
To equal part of next day
  • -2
Yaar itna simple hai
  • 0
Please find this answer

  • 1
Parallelogram side of trapezium 25and30 non parallel sides are 15 and 15 find the area of trapezium
  • 0
ABC is the triangle and AD be the median (which means BD =DC).

Construct AN perpendicular (90 degree) to BC.

Now ar(ABD) = ? AN x BD [1]

ar(ACD) = ? AN x CD [2]

We know that BD=CD ( since AD is the median)
Therefore ,from [1] and [2]
ar ( ABD) = ar(ACD)

=> Median of a triangle divides it into two triangles of equal area.
  • 0
By congurancy
  • 0
By congurant the triangles
  • 0
Please find this answer

  • 0
Please find this answer

  • 0
is Sawal ka answer bhejo

  • 0
Please find this answer

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