# If Ad is a Median of a Triangle Abc, Then Prove that Triangles Adb and Adc Are Equal in Area. If G is the Mid-point of Median Ad, Prove that Ar (δ Bgc) = 2 Ar (δ Agc). - Mathematics

If AD is a median of a triangle ABC, then prove that triangles ADB and ADC are equal in
area. If G is the mid-point of median AD, prove that ar (Δ BGC) = 2 ar (Δ AGC).

#### Solution

Draw AM ⊥ BC
Since, AD is the median of ΔABC

∴  BD = DC

⇒ BD = AM = DC × AM

⇒  1/2 (BD xx AM ) = 1/2 ( DC xx AM)

⇒ ar (Δ ABC)  = ar (Δ ACD)   ........ (1)

In ΔBGC , GDis the median

∴ ar (BGD)  = area (OGD)      ......... (2)

In ΔACD , CG is the median

∴ area (AGC)  = area (Δ CGD)  ......... (3)

From (1) and  (2) , we have

Area (ΔBGD) = ar (Δ AGC)

But, ar (ΔBGC) = 2ar (BGD)

∴  ar (BGC ) = 2ar (Δ AGC)

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 14 Areas of Parallelograms and Triangles
Exercise 14.3 | Q 10 | Page 45