1800-212-7858 (Toll Free)
9:00am - 8:00pm IST all days
8104911739

or

Thanks, You will receive a call shortly.
Customer Support

You are very important to us

022-62211530

Mon to Sat - 11 AM to 8 PM

# How can i prove that the medians of a triangle are concurrent for a class 9 standart?

Asked by ishitahazarika.i22 13th January 2019, 12:45 AM

Let D and E are mid point of side AC and side AB respectively. Let us join D and E as shown in left side of figure.
We know that since D and E are mid points two sides of triangle, line DE is parallel to third side BC and DE = (1/2)BC.

Since DE is parallel to BC, as marked in the figure, EDG = GBC and DEG = GCB .
Hence ΔGED and ΔGBC are similar triangles. we have
Hence the intersection point G divides the median BD and CE in the ratio 2:1  or GD = (1/3)BD  and GE = (1/3)CE

Now if we draw medians BD and AF as shown in right side of figure, we can similarly prove ΔGFD and ΔGAB are similar,
BD and AF intersects at G so that GF = (1/3)AF  and GD = (1/3)BD

since we have proved in both the cases,  if any two medians intersect, then intersection point divides the medians in the ratio 1:3,
hence all the three medians are concurrent
Answered by Expert 14th January 2019, 1:59 PM
• 1
• 2
• 3
• 4
• 5
• 6
• 7
• 8
• 9
• 10

You have rated this answer /10

RELATED STUDY RESOURCES :

### Latest Questions

CBSE IX History
Asked by n.p.roy1 17th August 2019, 4:55 PM
ICSE IX Chemistry
Asked by arpitaroy240187 17th August 2019, 4:52 PM