# In Fig. 9.24, ABC and ABD are two triangles on the same base AB. If line-segment CD is bisected by AB at O, show that ar(ABC) = ar (ABD).

**Solution:**

AB bisects CD at O signifies that O is the mid-point of CD. AO and BO are medians of triangles ADC and BDC.

Also, the median divides the triangle into two triangles of equal areas.

Consider ΔACD.

Line-segment CD is bisected by AB at O. Therefore, AO is the median of ΔACD.

∴ Area (ΔACO) = Area (ΔADO) ....(1)

Similarly, Considering ΔBCD , BO is the median.

∴ Area (ΔBCO) = Area (ΔBDO) ...( 2)

Adding equation (1) and equation (2), we obtain

Area (ΔACO) + Area (ΔBCO) = Area (ΔADO) + Area (ΔBDO)

⇒ Area (ΔABC) = Area (ΔABD)

**Video Solution:**

## In Fig. 9.24, ABC and ABD are two triangles on the same base AB. If line-segment CD is bisected by AB at O, show that ar(ABC) = ar (ABD).

### Maths NCERT Solutions Class 9 - Chapter 9 Exercise 9.3 Question 4:

**Summary:**

If ABC and ABD are two triangles on the same base AB, and line-segment CD is bisected by AB at O, then Area of (ABC) = Area of (ABD).