Home
Class 9
MATHS
The medians of Delta ABC intersect at po...

The medians of `Delta ABC` intersect at point G. Prove that:
area of `Delta AGB = (1)/(3) xx " area of " Delta ABC`

Text Solution

Verified by Experts

Let D is the mid-point of BC.
In `Delta ABC`
D is the mid-point of BC
`:.` area of `Delta ABD = " area of " Delta ADC`
(`.:` Median divides the triangle into two equal area)..(1)
In `Delta GBC`
D is the mid-point of BC
`:.` area of `DeltaGBD = " area of " Delta GCD`
(`.:` median divides the triangle into two equal area)..(2)
Subtract (2) from (1), we get
area of `Delta ABD - " area of " DeltaGBD = " area of "DeltaACD - " area of "Delta GCD`
`rArr` area of `DeltaABG = " area of " Delta ACG`....(3)
Similarly, we can prove that
area of `DeltaACG = " area of " DeltaBCG`
(`:.` median divides the triangle into two equal area)...(4)
From (3) and (4), we get
area of `DeltaABG = " area of "DeltaACG = " area of " DeltaBCG`
`:.` area of `Delta ABG = (1)/(3) xx " area of " Delta ABC`
Promotional Banner

Topper's Solved these Questions

  • AREA OF PARALLELOGRAMS AND TRIANGLES

    NAGEEN PRAKASHAN|Exercise Problems From NCERT/exemplar|12 Videos

  • AREA OF PARALLELOGRAMS AND TRIANGLES

    NAGEEN PRAKASHAN|Exercise Exercise|34 Videos

  • CIRCLE

    NAGEEN PRAKASHAN|Exercise Revision Exercise (long Answer Questions )|5 Videos

Similar Questions

Explore conceptually related problems

In the adjoining figure, AD is the median of Delta ABC and X be any point on side AD. Prove that: area (Delta ABX) = " area " (Delta ACX)

The median BE and CF of a triangle ABC intersect at G. Prove that the area of DeltaGBC = area of the quadrilateral AFGE.

D is the mid-point of side AB of the triangle ABC.E is the mid-point of CD and F is the mid-point of AE. Prove that 8 xx " area of " (DeltaAFD) = " area of " Delta ABC

Three medians AD, BE and CF of Delta ABC intersect at G. The area of Delta ABC is 36 sq. cm. Then the area of Delta CGE is

In the adjoining figure, D is the mid-point of side AB of Delta ABC and P be any point on side BC. If CQ ||PD , then prove that: area of Delta BPQ = (1)/(2) xx " area of " Delta ABC

D is a point on the base BC of Delta ABC.AD is produced upto E such that DE = AD. Prove that: area of Delta BCE = " area of " Delta ABC

In the adjoining figure, BD = DC and AE = ED. Prove that area of Delta ACE = (1)/(4) " area of " Delta ABC

The three medians AD, BE and CF of Delta ABC intersect at point G. If the area of DeltaABC is 60 sq.cm. then the area of the quadrilateral BDGF is :

The medians BE and CF of a triangle ABC intersect at G. Prove that area of hat varphi GBC=area of quadrilateral AGFE

If the median AD and BE of a triangle ABC intersect at 0 ,prove that area of Delta AOB= area of quadrilateral CDOE.