Question -
Answer -
Given:
(1) ABC and ABD are two triangles on the same base AB,
(2) CD bisect AB at O which means AO = OB
To Prove: Area of ΔABC = Area of ΔABD
Proof:
Here it is given that CD bisected by AB at O which means O is the midpoint of CD.
Therefore AO is the median of triangle ACD.
Since the median divides a triangle in two triangles ofequal area
Therefore Area of ÄCAO = Area of ÄAOD ......(1)
Similarly for Δ CBD, O is the midpoint of CD
Therefore BO is the median of triangle BCD.
Therefore Area of ÄCOB = Area of ÄBOD ......(2)
Adding equation (1) and (2) we get
Area of ΔCAO + Area of ΔCOB = Area of ΔAOD + Area of ΔBOD
⇒ Areaof ÄABC =Area of ÄABD
Hence it is proved that 