# 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

Consider a triangle ABC Let D be the midpoint of E be the midpoint of F be the midpoint of , and O be the centroid.

By definition, . Thus[ADO] = [BDO],[AFO] = [CFO],[BEO] = [CEO], and , where [ABC] represents the area of triangle ; 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:  Thus, and Since , therefore, . Using the same method, you can show that • -2

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 

ar(ACD) = ½ AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 

ar(ACD) = � AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 • -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 • 12
ravinda mirinda
• -2
hi
• -14
hii
• -13
Hello
• -13
Here ABC is a triangle
consider the two triangles
from this,
AB=AC     sides
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 

ar(ACD) = ½ AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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  ar(ACD) = � AN x CD  We know that BD=CD ( since AD is the median) Therefore ,from  and  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 • 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 

ar(ACD) = ? AN x CD 

We know that BD=CD ( since AD is the median)
Therefore ,from  and 
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 • 0 • 0  